Publikationen
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Zur Veröffentlichung eingereichte Fachberichte
- Wavenumber-explicit stablity and convergence analysis of hp-finite element discretizations of Helmholtz problems in piecewise smooth media
 M. Bernkopf, T. Chaumont-Frelet, J.M. Melenk
 arXiv:2209.03601[math.NA]
- Exponential convergence of a generalized FEM for heterogeneous reaction-diffusion equations
 C.P. Ma, J.M. Melenk
 arXiv:2209.01957[math.NA]
- On interpolation spaces of piecewise polynomials on mixed meshes
 M. Karkulik, J.M. Melenk, A. Rieder
 arXiv:2306.169907[math.NA]
- Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides
 J.M. Melenk, L. Demkowicz, S. Henneking
 arXiv:2307.04521[math.NA]
- Stability Analysis for Electromagnetic Waveguides. Part 2: Nonhomogeneous Waveguides
 L. Demkowicz, J.M. Melenk, J. Badger, S. Henneking
 Oden Institute Report 23-3
- Weighted analytic regularity for the integral fractional Laplacian in polyhedra
 Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab
 arXiv:2307.11679[AP]
Buch
- hp-finite element methods for singular perturbations
 Springer LNM 1796 (2002) © Springer-Verlag, 318pp.
 Errata (nicht verfügbar)
Sammelbänder
- Direct and Inverse Problems in Wave Propagation and Applications  
 (I.G. Graham, U. Langer, J.M. Melenk, M. Sini editors)
 Radon Series on Computational and Applied Mathematics , Vol. 14
 DeGruyter (2013), ISBN: 978-3-11-028228-3
- Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1  
 (J.M. Melenk, I. Perugia, J. Schöberl, C. Schwab editors)
 Springer Lecture Notes in Computational Sciences, 137
 Springer (2023), ISBN: 978-3-031-20431-9 (hardcover), 978-3-031-20434-0 (softcover) 978-3-031-20432-6 (ebook)
Herausgegebene Journal-Sonderausgabe
- Invited Papers from the WAVES 2019 conference  
 (M. Kaltenbacher and J.M. Melenk editors) Springer-Nature Partial Differential Equations and Applications (2020)
Buchkapitel
- Interpolation and quasi-interpolation in h- and hp-version finite element spaces  
 T. Apel, J.M. Melenk
 in: Encyclopedia of Computational Mechanics, second edition, E. Stein, R. de Borst, T. Hughes (eds.), 2017, ISBN: 978-1-119-00379-3, pp. 1-33
 extended preprint version available as ASC Report 39/2015 (PDF)
- hp-Version of Finite Element Method  
 in: Encyclopedia of Applied and Computational Mathematics, B. Engquist (ed.), 2016, pp. 656-659, ISBN 978-3-540-70528-4 (Print) 978-3-540-70529-1 (Online)
- On stability of discretizations of the Helmholtz equation  
 S. Esterhazy, J.M. Melenk
 in: Numerical Analysis of Multiscale Problems, I.G. Graham, T.Y. Hou, O. Lakkis, R. Scheichl (Eds.),
 Springer LNCSE 83 (2012), pp. 285-324
 extended version available as ASC Report 01/2011 (PDF) or at arXiv:1105.2112v2 [math.NA]
- On Approximation in Meshless Methods  
 in: Frontiers in Numerical Analysis, Durham 2004, J. Blowey, A. Craig (eds.), Springer Verlag 2005, pp. 65-141
 available as preprint 11/2004 (PDF)
(Hinweis: In der Regel liegt das Urheberrecht der nachstehenden Dokumente beim Herausgeber - die Links mit der DOI verweisen auf die veröffentlichten Versionen. Die Links zu den früheren technischen Berichten können von den veröffentlichten Endversionen abweichen.)
Begutachtete Artikel
- Exponential convergence of hp-FEM for the integral fractional Laplacian in polygons
 M. Faustmann, C. Marcati, J.M. Melenk, C. Schwab
 to appear in SIAM J. Numer. Anal.
 arXiv:2209.11468[math.NA]
- Wavenumber-explicit hp-FEM analysis for Maxwell's equations with impedance boundary conditions
 J.M. Melenk, S. Sauter
 to appear in Found. Comp. Math.
 arXiv:2201.02602[math.NA]
- Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs
 R. Becker, M. Brunner, M. Innerberger, J.M. Melenk, D. Praetorius
 M2AN 57 (2023), pp. 2193-2225
 arXiv:2211.04123[math.NA]
- H-inverses for RBF interpolation
 N. Angleitner, M. Faustmann, J.M. Melenk
 to appear in Adv. Comp. Math.
 arXiv:2109.05763[math.NA]
- Exponential meshes and H-matrices
 N. Angleitner, M. Faustmann, J.M. Melenk
 Comput. Math. Appl. 130 (2023) pp. 21-40
 arXiv:2203.09925[math.NA]
- hp-FEM for reaction-diffusion equations. II. robust exponential convergence for multiple length scales in corner domains.
 L. Banjai, J.M. Melenk, C. Schwab
 in press in IMA J. Numer. Anal.
 ASC Report 11/2020 (PDF) or at arXiv:2004.10517[math.NA]
- An exponentially convergent discretization for space-time fractional parabolic equations using hp-FEM
 J.M. Melenk, A. Rieder
 in press in IMA J. Numer. Anal.
 arXiv:2202.02067[math.NA]
- Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D
 B. Bahr, M. Faustmann, C. Marcati, J.M. Melenk, C. Schwab
 in: ICOSAHOM 2020+1 , (Melenk, Perugia, Schöberl, Schwab eds) Springer LCSE 137 pp. 291-306
 arXiv:2204.04113[math.NA]
- Exponential convergence of hp-FEM for spectral fractional diffusion in polygons
 L. Banjai, J.M. Melenk, C. Schwab
 Numer. Math. 153 (2023), pp. 1-47
 ASC Report 30/2020 (PDF) or at arXiv:2011.05701[math.NA]
- Optimal convergence rates for a first order system least squares method. Part I: homogeneous boundary conditions
 M. Bernkopf, J.M. Melenk
 to appear in M2AN 57 (2023), pp. 107-141
 ASC Report 45/2020 (PDF) or at arXiv:2012.12919[math.NA]
- Weighted analytic regularity for the integral fractional Laplacian in polygons
 M. Faustmann, J.M. Melenk, C. Marcati, C. Schwab
 SIAM J. Math. Anal. 54 (2022) pp. 6323-6357
 arXiv:2112.08151[math.AP]
- Goal-oriented adaptive finite element method for semilinear elliptic PDEs
 R. Becker, M. Brunner, M. Innerberger, J.M. Melenk, D. Praetorius
 Comput. Math. Appl. 118 (2022), pp. 18--35
 arXiv:2112.06687[math.NA]
- Mortar coupling of hp-discontinuous Galerkin and boundary element methods for the Helmholtz equation
 C. Erath, L. Mascotto, J.M. Melenk, I. Perugia, A. Rieder
 J. Sci. Comp. 92:1 (2022), paper nr. 2
 arXiv:2105.06173[math.NA]
- H-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equation
 M. Faustmann, J.M. Melenk, M. Parvizi
 Adv. Comp. Math. 48 (2022) article nr. 59
 preprint at arXiv:2103.14981[math.NA]
- Time domain boundary integral equations and convolution quadrature for scattering by composite media
 A. Rieder, F.-J. Sayas, J.M. Melenk
 Math. Comp. 337 (2022), pp. 2165-2195
 ASC Report 29/2020 (PDF) or at arXiv:2010.14162[math.NA]
- Caccioppoli-type estimates and H-Matrix approximations to inverses for FEM-BEM couplings
 M. Faustmann, J.M. Melenk, M. Parvizi
 Numer. Math. 150 (2022), pp. 849-892
 ASC Report 20/2020 (PDF) or at arXiv:2008.11498[math.NA]
- Local convergence of the FEM for the integral fractional Laplacian
 M. Faustmann, M. Karkulik, J.M. Melenk
 SIAM J. Numer. Anal. 60 (2022), pp. 1055-1082
 ASC Report 24/2020 (PDF) or at arXiv:2005.14109[math.NA]
- Metastable Speeds in the Fractional Allen-Cahn Equation
 F. Achleitner, C. Kuehn, J.M. Melenk, A. Rieder
 Appl. Math. Comp. 408 (2021) Paper nr. 126329
 ASC Report 13/2020 (PDF) or at arXiv:2006.02731[math.DS]
- Approximating inverse FEM matrices on non-uniform meshes with H-matrices
 N. Angleitner, M. Faustmann, J.M. Melenk
 Calcolo 58 (2021), Paper nr. 3
 ASC Report 14/2020 (PDF) or at arXiv:2005.04999[math.NA]
- Runge-Kutta approximation for \(C_0\)-semigroups in the graph norm with applications to time domain boundary integral equations
 A. Rieder, F.-J., Sayas, J.M. Melenk
 SN PDEs and Applications 1 (2020), Paper nr. 49
 ASC Report 06/2020 (PDF) or at arXiv:2003.01996[math.NA]
- On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion
 M. Faustmann, J.M. Melenk, M. Parvizi
 M2AN 55 (2021), pp. 595-625
 ASC Report 03/2020 (PDF) or at arXiv:1912.09160[math.NA]
- On superconvergence of Runge-Kutta convolution quadrature for the wave equation
 J.M. Melenk, A. Rieder
 Numer. Math. 147 (2021), p. 157--188
 ASC Report 13/2019 (PDF) or at arXiv:1904.00847[math.NA]
- Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian
 M. Faustmann, J.M. Melenk, D. Praetorius
 Math. Comp. 90 (2021) pp. 1557-1587
 ASC Report 07/2019 (PDF) or at arXiv:1903.10409[math.NA]
- Wavenumber-explicit hp-FEM analysis for Maxwell's equations with transparent boundary conditions
 J.M. Melenk, S.A. Sauter
 Found. Comp. Math. 21 (2021), pp. 125-241
 available at ASC Report 09/2018 (PDF) or at arXiv:1803.01619[math.NA]
- \(hp\)-FEM for the fractional heat equation
 J.M. Melenk, A. Rieder
 IMA J. Numer. Anal. 41 (2021), pp. 412-454
 available at ASC Report 12/2019 (PDF) or at arXiv:1901.01767[math.NA]
- Wave number-Explicit Analysis for Galerkin Discretizations of Lossy Helmholtz Problems
 J.M. Melenk, S.A. Sauter, C. Torres
 SIAM J. Numer. Anal. 54 (2020), 2119-2143
 available at ASC Report 11/2019 (PDF) or at arXiv:1904.00207[math.NA]
- FEM-BEM mortar coupling for the Helmholtz equation in three dimensions
 L. Mascotto, J.M. Melenk, I. Perugia, A. Rieder
 Comp. Math. Appl. 80 (2020), pp. 2351-2378
 available at ASC Report 08/2020 (PDF) or at arXiv:2004.03523[math.NA]
- Stable decompositions of \(hp\)-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D
 M. Karkulik, J.M. Melenk, A. Rieder
 M2AN 54 (2020), pp. 145-180
 available at ASC Report 25/2018 (PDF) or at arXiv:1811.11097[math.NA]
- On commuting p-version projection-based interpolation on tetrahedra
 J.M. Melenk, C. Rojik
 Math. comp. 89 (2020), pp. 45-87
 extended version available at ASC Report 05/2018 (PDF) or at arXiv:1802.00197[math.NA]
- H-matrix approximability of inverses of discretizations of the fractional Laplacian
 M. Karkulik and J.M. Melenk
 Adv. Comp. Math. 45 (2019), pp. 2893-2919
 ASC Report 25/2018 (PDF) or at arXiv:1808.04274[math.NA]
- Analysis of the hp-version of a first order system least squares method for the Helmholtz equation
 M. Bernkopf and J.M. Melenk
 in: Advanced Finite Element Methods with Applications - Selected Papers from the 30th Chemnitz FEM Symposium 2017 (T. Apel, U. Langer, A. Meyer, O. Steinbach eds.), Springer LNCSE 128 (2019), pp. 57-84
 available ASC Report 24/2018 (PDF) or at arXiv:1808.07825[math.NA]
- Tensor FEM for spectral fractional diffusion
 L. Banjai, J.M. Melenk, R.H. Nochetto, E. Otárola, A. Salgado, C. Schwab
 Found. Comp. Math. 19 (2019), pp.901-962
 available as ASC Report 13/2017 (PDF) or at arXiv:1707.07367[math.NA]
- Local convergence of the BEM on polyhedral domains
 M. Faustmann, J.M. Melenk
 Numer. Math. 140 (2018), pp. 593-637
 available as ASC Report 03/2017 (PDF) or at arXiv:1702.04224[math.NA]
- On thin plate spline interpolation
 M. Löhndorf, J.M. Melenk
 ICOSAHOM 2016, Springer LNCSE 119, M. Bittencourt, N. Dumont, J. Hesthaven (eds), pp. 451--466
 available as ASC Report 09/2017 (PDF) or at arXiv:1705.05178[math.NA]
- An analysis of a butterfly algorithm
 S. Börm, C. Börst, J.M. Melenk
 Comp. Math. Appl. 74 (2017), pp. 2125-2143
 available at arXiv:1703.01941 or as ASC report 12/2017 (PDF)
- Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains
 M. Faustmann, J.M. Melenk
 Comp. Math. Appl. 74 (2017) pp. 1576-1589
 ASC Report 25/2016 (PDF) or at arXiv:1610.09211[math.NA]
- Approximation of the high-frequency Helmholtz kernel by nested directional interpolation
 S. Börm, J.M. Melenk
 Numer. Math. 137 (2017), pp. 1-34
 ASC Report 33/2015 (PDF) or at arXiv:1510.07189[math.NA]
- Runge-Kutta convolution quadrature and FEM-BEM coupling for the time-dependent linear Schrödinger equation
 J.M. Melenk, A. Rieder
 J. Integral equations and applications 29 (2017), pp. 189-250
 ASC Report 13/2016 (PDF) or at arXiv:1605.07340[math.NA]
- Simultaneous quasi-optimal convergence rates in FEM-BEM coupling
 J.M. Melenk, D. Praetorius, B. Wohlmuth
 Math. Methods. Appl. Sci. 40 (2017), pp. 463-485
 also available as ASC Report 13/2014 (PDF) or at arXiv:1404.2744 [math.NA]
- An hp-Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems
 M. Amrein, J.M. Melenk, T. Wihler
 Math. Methods Appl. Sci. 40 (2017), pp 1973-1985
 available at ASC Report 06/2016 (PDF) or at arXiv:1602.05354[math.NA]
- Local inverse estimates for non-local boundary integral operators
 M. Aurada, M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius
 Math. Comp. 86 (2017), pp. 2651-2686
 available as ASC Report 12/2015 (PDF) or at arXiv:1504.04394 [math.NA]
- Existence of H-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator
 M. Faustmann, J.M. Melenk, D. Praetorius
 IMA J. Numer. Anal. 37 (2017) pp. 1211-1244
 available as ASC Report 08/2015 (PDF) or at arXiv:1503.01943[math.NA]
- Existence of H-matrix approximants to the inverses of BEM matrices: the simple-layer operator
 M. Faustmann, J.M. Melenk, D. Praetorius
 Math. Comp. 85 (2016), pp 119-152
 also available as ASC Report 37/2013 (PDF) and arXiv:1311.5028 [math.NA]
- Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion equations
 J.M. Melenk, C. Xenophontos
 Calcolo 53 (2016), pp. 105-132
 available as ASC Report 24/2014 (PDF) or at arXiv:1408.3328[math.NA]
- Local high-order regularization and applications to hp-methods
 M. Karkulik, J.M. Melenk
 Comp. Math. Appl. 70 (2015), pp. 1606-1639
 preprint version available as
 ASC Report 38/2014 (PDF) or at arXiv:1411.5209[math.NA]
- Optimal additive Schwarz methods for the hp-BEM: the hypersingular integral operator in 3D on locally refined meshes
 T. Führer, J.M. Melenk, D. Praetorius, A. Rieder
 Comp. Math. Appl. 70 (2015), pp. 1583-1605
 available as ASC Report 41/2014 (PDF) or at arXiv:1412.2024[math.NA]
- On optimal L^2 and surface flux convergence in FEM
 T. Horger, J.M. Melenk, B. Wohlmuth
 CVS 16 (2013), pp. 231-246
 ASC Report 02/2015 (PDF) or at arXiv:1501.03003 [math.NA]
- When is the error in the h-BEM for solving the Helmholtz equation bounded independently of k?
 I.G. Graham, M. Löhndorf, J.M. Melenk, E.A. Spence
 BIT 55 (2015), pp. 171-214
 ASC Report 28/2013 (PDF)
- H-matrix approximability of the inverse of FEM matrices
 M. Faustmann, J.M. Melenk, D. Praetorius
 Numer. Math. 131 (2015), pp. 615-642
 available as ASC Report 20/2013 (PDF) and arXiv:1308.0499 [math.NA]
- FEM-BEM coupling for the large-body limit in micromagnetics
 M. Aurada, J.M. Melenk, D. Praetorius
 J. Comp. Math. 281 (2015), pp. 10-31
 also available as ASC Report 4/2013 (PDF)
- Quasi-optimal convergence rates for adaptive BEMs with data approximation. Part II: hyper-singular integral equation
 M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius
 Electron. Trans. Numer. Anal 44 (2015), pp. 153-176
 also available as ASC Report 30/2013 (PDF)
- A scalable numerical approach for the Steady-State Ab-Initio Laser Theory
 S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K.G. Makris, A.D. Stone, J.M. Melenk, S.G. Johnson, S. Rotter
 Phys. Rev. A 90 023816 (2014)
 also available as ASC Report 40/2013 (PDF) and arXiv:1312.2488 [physics.optics]
- On the stability of the boundary trace of the polynomial L^2 projection on triangles and tetrahedra
 J.M. Melenk, T. Wurzer
 Comp. Math. Appl. 67 (2014), pp. 944-965
 also available as extended versions (with slightly different title) at ASC Report 25/2012 (PDF) or arXiv:1302.7189 [math.NA]
- An analysis of discretizations of the Helmholtz equation in L^2 and in negative norms
 S. Esterhazy, J.M. Melenk
 Comp. Math. Appl. 67 (2014), pp. 830-853
 extended version available as ASC Report 31/2012 (PDF) or as corrected version (PS)
- Quasi-optimal convergence rates for adaptive BEMs with data approximation. Part I: weakly singular integral equations
 M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius
 Calcolo 51 (2014), pp. 531--562
 available as ASC Report 24/2013 (PDF)
- Mixed conforming elements for the large-body limit in micromagnetics
 M. Aurada, J.M. Melenk, D. Praetorius
 M3AS 24 (2014), pp. 113--144
 available (with a different title) as ASC Report 42/2011 (PDF)
- Quasi-optimal a priori estimates for fluxes in mixed finite element methods and applications to the Stokes--Darcy coupling
 J.M. Melenk, H. Rezaijafari, B. Wohlmuth
 IMA J. Numer. Anal. 34 (2014), pp. 1-27
 available as ASC Report 05/2012 (PDF)
- General DG-Methods for Highly Indefinite Helmholtz Problems
 J.M. Melenk, A. Parsania, S. Sauter
 J. Sci. Comp. 57 (2013), pp. 536-581
 available as corrected version (PS) of ASC Report 06/2012 (PDF) (with slightly different title)
- Symmetry-free, p-robust equilibrated error indication for the hp-version of the FEM in almost incompressible linear elasticity
 P. Dörsek, J.M. Melenk
 CMAM 13 (2013), pp 291--304
 available as ASC Report 46/2012 (PDF)
- A numerical study of averaging error indicators in p-FEM
 P. Dörsek, J.M. Melenk
 in: Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012,
 Azaiez, M., El Fekih, H., Hesthaven, J. (eds), LCSE 95, Springer, 2014, pp. 227-236
 available as ASC Report 45/2012 (PDF)
- Quasi-optimal convergence rate for an adaptive boundary element method
 M. Feischl, M. Karkulik, J.M. Melenk, D. Praetorius
 SIAM J. Numer. Anal. 51 (2013), pp. 1327--1348
 available as ASC Report 28/2011 (PDF)
- A high frequency hp-boundary element method for scattering by convex polygons
 D.P. Hewett, S. Langdon, J.M. Melenk
 SIAM J. Numer. Anal. 51 (2013), pp. 629--653
 available as ASC Report 40/2011 (PDF)
- Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: a roadmap
 J.M. Melenk, C. Xenophontos, L. Oberbroeckling
 Adv. Comp. Math. 39 (2013), pp. 367-394
 available as extended version (with slightly different title): as ASC Report 29/2011 (PDF) and at arXiv:1108.2002 [math.NA]
- Robust exponential convergence of hp-FEM for singularly perturbed reaction-diffusion systems with multiple scales
 J.M. Melenk, C. Xenophontos, L. Oberbroeckling
 IMA J. Numer. Anal. 33 (2013), pp. 609--628
 available as revised version (PS) of ASC Report 31/2011 (PDF)
- Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity
 M. Aurada, M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius
 Comp. Mech. 51 (2013), pp. 399--419
 available as ASC Report 08/2012 (PDF) or at arXiv:1211.4225 [math.NA]
- Quasi-optimal approximation of surface based Lagrange multipliers in finite element methods
 J.M. Melenk, B. Wohlmuth
 SIAM J. Numer. Anal. 50 (2012), pp. 2064--2087
 available as ASC Report 13/2011 (PDF) and as corrected version (PS)
- Mapping properties of combined field Helmholtz boundary integral operators
 SIAM J. Math. Anal. 44 (2012), pp. 2599--2636
 corrected version (PS) of ASC Report 01/2010 (PDF)
- Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics
 S. Ferraz-Leite, J.M. Melenk, D. Praetorius
 Numer. Math. 122 (2012), pp. 101--131
 available as ASC Report 32/2011 (PDF)
- Wavenumber-explicit hp-BEM for high frequency scattering
 M. Löhndorf, J.M. Melenk
 SIAM J. Numer. Anal. 49 (2011), pp. 2340--2363
 available as corrected version (PS) of ASC Report 02/2010 (PDF)
- Wavenumber explicit convergence analysis for Galerkin discretizations of the Helmholtz equation
 J.M. Melenk, S. Sauter
 SIAM J. Numer. Anal. 49 (2011), pp. 1210--1243
 extended version available as corrected version (PS) of ASC Report 31/2009 (PDF)
- Runge-Kutta convolution quadrature for operators arising in wave propagation
 L. Banjai, C. Lubich, J.M. Melenk
 Numer. Math., 119 (2011), pp. 1-20
 available as ASC Report 24/2010 (PDF)
- Adaptive hp-FEM for the contact problem with Tresca friction in linear elasticity: the primal-dual formulation and a posteriori error estimation
 P. Dörsek, J.M. Melenk
 Appl. Numer. Math. 60 (2010), pp. 689--704
 extended version available as ASC Report 37/2009 (PDF)
- hp-FEM for the contact problem with Tresca friction in linear elasticity: the primal formulation
 P. Dörsek, J.M. Melenk
 in: Spectral and high order methods for PDEs, J. Hesthaven, E. Rønquist eds, pp. 1-17, LNCSE 76, Springer Verlag (2011)
 extended version available as ASC Report 36/2009 (PDF)
- Convergence Analysis for Finite Element Discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions
 J.M. Melenk, S. Sauter
 Math. Comp. 79 (2010), pp. 1871--1914
 available as revised version (PDF) of ASC Report 15/2008 (PDF)
- Optimal Convergence of Higher Order Finite Element Methods for Elliptic Interface Problems
 Jingzhi Li, J.M. Melenk, Barbara Wohlmuth, Jun Zou
 Appl. Numer. Math. , 60 (2010), pp. 19--37
 available as revised version (PS) of ASC Report 13/2008 (PDF)
- On the suboptimality of the p-version interior penalty discontinuous Galerkin method
 E. Georgoulis, E. Hall, J.M. Melenk
 J. Sci. Comp. 42 (2010), pp. 54-67
 available as ASC Report 03/2009 (PDF)
- On the convergence of Filon quadrature
 J. Comput. Appl. Math. , 234 (2010), pp. 1692--1701
 extended version available as ASC Report 08/2008 (PDF)
- p-FEM quadrature error analysis on tetrahedra
 T. Eibner, J.M. Melenk, in: Proceedings of DD17, Langer, Discacciati, Keyes, Widlund, Zulehner (eds.), Springer LNSCE vol. 60 (2008), pp. 493-500 (ISSN 1439-7358)
 available as ASC Report 23/2007 (PDF)
- Multilevel preconditioning for the boundary concentrated hp-FEM
 T. Eibner, J.M. Melenk
 Comp. Meth. Mech. Eng. 196 (2007), pp. 3713-3725
 available as Preprint 05-13 (PS) of the SFB 393
- Additive Schwarz preconditioning for p-version triangular and tetrahedral finite elements
 J. Schöberl, J.M. Melenk, C. Pechstein, S. Zaglmayr,
 IMA J. Numer. Anal. 28 (2008), pp. 1-24
 this article was among the top 5 downloads in 2008
 available as Preprint 11/2005 of the Radon institute
- Fast algorithms for setting up the stiffness matrix in hp-FEM: a comparison
 T. Eibner, J.M. Melenk
 preprint version (PS)
 in: Computer Mathematics and its Applications-Advances and Developments (1994-2005), Elias A. Lipitakis (Ed.), LEA Publ., Athens, Greece, pp. 575-596, ISBN: 960-87275-9-6
- An adaptive strategy for hp-FEM based on testing for analyticity
 T. Eibner and J.M. Melenk
 Comp. Mech. 39 (2007), pp. 575-595
 preprint version (PDF)
- A local error analysis of the boundary concentrated FEM
 T. Eibner and J.M. Melenk
 IMA J. Numer. Anal. 26 (2006), pp.752-778
 preprint version (PS)
- hp-interpolation of non-smooth functions
 SIAM J. Numer. Anal. 43 (2005), pp. 127-155
 extended version is available as
 Preprint NI03050 of the Isaac Newton Institute for Mathematical Sciences
- Approximation of integral operators by variable-order interpolation
 S. Börm, M. Löhndorf, J.M. Melenk
 Numer. Math. 99 (2005), pp. 605-643
 preprint version
- Mortar methods with curved interfaces
 B. Flemisch, J.M. Melenk, B. Wohlmuth,
 Appl. Numer. Math. 54 (2005), pp. 339-361
 preprint version
- Two-scale regularity for homogenization problems with non-smooth fine scale geometry
 A.-M. Matache & J.M. Melenk
 M3AS, 13 (2003), pp. 1053-1080
 available as Preprint 63 (PS) of the DFG priority program "multiscale problems"
- Boundary concentrated FEM
 B.I. Khoromskij & J.M. Melenk,
 SIAM J. Numer. Anal. 41 (2003), pp. 1-36
 preprint version
- An efficient direct solver for the boundary concentrated FEM in 2D
 B.I. Khoromskij & J.M. Melenk,
 Computing 69 (2002), pp. 91-117
 preprint version
- On condition numbers in hp-FEM with Gauß-Lobatto based shape functions
 J. Comput. Appl. Math. , 139 (2002), pp. 21-48
 preprint version (PS.GZ)
- On residual-based aposteriori error estimation in hp -FEM
 J.M. Melenk & B. Wohlmuth,
 Advances in Comput. Math. , 15 (2001), pp. 311-331
 preprint version (PS.GZ)
- Approximation orders for natural splines in arbitrary dimensions
 J.M. Melenk & T. Gutzmer,
 Math. Comput. 70 (2001), pp. 699-703
 preprint version (PS.GZ)
- Fully discrete hp finite elements: fast quadrature
 J.M. Melenk, K. Gerdes, & C. Schwab,
 Comput. Meths. Appl. Mech. Engrg. 190 (2001), pp. 4339-4364
 preprint version
- The hp-version of the Streamline Diffusion Finite Element Method in two dimensions,
 K. Gerdes, J.M. Melenk, D. Schötzau, & C. Schwab,
 M3AS 11 (2001), pp. 301-337
 abstract and paper
- Spectral Galerkin discretizations for hydrodynamic stability problems
 J.M. Melenk, N.P. Kirchner, & C. Schwab,
 Computing 65 (2000), p. 97-118
 abstract and paper
- On n-widths for elliptic problems
 J. Math. Anal. Appl. 247 (2000), p. 272-289
 preprint version (PS.GZ)
- The hp-Streamline Diffusion Method for Convection Dominated Problems in One Space Dimension
 J.M. Melenk & C. Schwab,
 East-West J. Numer. Math. 7 (1999), 31-60
 abstract and paper
- Operator adapted spectral element methods. I: harmonic and generalized harmonic polynomials
 Numer. Math. 84 (1999), p. 35-69
 preprint version
- An hp FEM for convection-diffusion problems in one dimension
 J.M. Melenk & C. Schwab,
 IMA J. Numer. Anal. 19 (1999), 425-453
 abstract and paper
- Analytic regularity for a singularly perturbed problem
 J.M. Melenk & C. Schwab,
 SIAM J. Math. Anal., 30 (1999), 379-400
 preprint version
- hp-FEM for Reaction-Diffusion Equations. I: Robust Exponential Convergence
 J.M. Melenk & C. Schwab,
 SIAM J. Numer. Anal., 35 (1998), 1520-1557
 preprint version
- On the Robust Exponential Convergence of hp-FEMs for Problems with Boundary Layers
 IMA J. Numer. Anal., 17 (1997), 577-601
 abstract and paper
- Approximation with harmonic and generalized harmonic polynomials in the partition of unity method
 J.M. Melenk & I. Babuska
 Comput. Assist. Mech. Eng. Sci. 4 (1997), 607-632
 Load Postscript (PS.GZ)
- The Partition of Unity Method
 I. Babuska & J.M. Melenk,
 Int. J. Numer. Meths. Eng., 40 (1997), 727-758
 preprint version (PS.GZ)
- The Partition of Unity Finite Element Method: Basic Theory and Applications
 J.M. Melenk & I. Babuska,
 Comput. Meths. Appl. Mech. Engrg.,139 (1996), 289-314
 abstract and paper
- Finite Element Method for Solving Problems with Singular Solutions
 I. Babuska, B. Andersson, B. Guo, J.M. Melenk, & H.-S. Oh,
 J. Comput. Appl. Math. , 74 (1996),51-70
 preprint version (PS.GZ)
- Functions with time- and frequency-gaps
 J.M. Melenk & G. Zimmermann,
 J. Fourier Anal. Appl. , 2 (6), 1996
 preprint version (PS.GZ)
Arbeiten
- hp-Finite Element Methods for Singular Perturbations (PS.GZ)
 Habilitationsschrift 2000
- On Generalized Finite Element Methods (PS.GZ)
 Dissertation 1995
- Finite element methods with harmonic shape functions for solving Laplace's equation (PS.GZ)
 MA-Arbeit 1992
Ausgewählte Beiträge zu Proceedings
- Optimally truncated WKB approximation for the highly oscillatory stationary 1D Schrödinger equation
 J. Körner, A. Arnold,C. Klein, J.M. Melenk
 extended abstract for ICNAAM 2023
 arXiv 2310.00955
- hp-FEM for the spectral fractional Laplacian
 L. Banjai, J.M. Melenk, C. Schwab
 Oberwolfach Report , 2019/40
- hp-FEM and hp-DGFEM for Helmholtz problems
 S. Esterhazy, J.M. Melenk, A. Parsania, S. Sauter
 Oberwolfach Report , 2013/03
- H-matrix approximability of the inverses of first kind BEM matrices
 M. Faustmann, J.M. Melenk, and D. Praetorius
 Oberwolfach Report , 2012/55
- A new proof for existence of H-matrix approximants to the inverse of FEM matrices: the Dirichlet problem for the Laplacian.
 M. Faustmann, J.M. Melenk, and D. Praetorius
 in: Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012,
 Azaiez, M., El Fekih, H., Hesthaven, J. (eds), LCSE 95, Springer, 2014, pp. 249-259
 ASC Report 51/2012 (PDF)
- novel inverse estimates for non-local operators
 M. Feischl, Tührer, M. Karkulik, J. Melenk, D. Praetorius:
 extended abstract for IABEM 2012
 ASC Report 49/2012 (PDF)
- FEM-BEM Couplings without Stabilization
 M. Feischl, T. Führer, M. Karkulik, J. Melenk, D. Praetorius:
 extended abstract for IABEM 2012
 ASC Report 47/2012 (PDF)
- Mixed Conforming Elements for the Large-Body Limit in Micromagnetics
 M. Aurada, J.M. Melenk, D. Praetorius
 proceedings of MathMod 2009
 ASC Report 49/2009 (PDF)
- Reduced Model in Thin-Film Micromagnetics
 S. Ferraz-Leite, J.M. Melenk, D. Praetorius
 proceedings of MathMod 2009
 ASC Report 02/2009 (PDF)
- Residual a-posteriori error estimates in BEM: Convergence of h-adaptive algorithms
 M. Feischl, M. Karkulik, J. Melenk, D. Praetorius:
 extended abstract for IABEM 2009
Unveröffentlichte Fachberichte und ausgewählte BA- und MA-Arbeiten
- mapping properties of Helmholtz boundary integral operators and their application to the hp-BEM
 M. Löhndorf and J.M. Melenk
 ASC Report 34/2009 (PDF)
- stability of the trace of the polynomial L2 projection on triangles
 Bachelor thesis of T. Wurzer
 ASC Report 36/2010 (PDF)
 an extended version that includes the 3D case is at arXiv:1302.7189 [math.NA]
- Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: proofs
 J.M. Melenk, C. Xenophontos, L. Oberbroeckling
 ASC Report 29/2011 (PDF) and at arXiv:1108.2002 [math.NA]
- Inverse estimates for elliptic integral operators and their application to the adaptive coupling of FEM and BEM
 M. Aurada, M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius
 ASC Report 07/2012 (PDF) or at arXiv:1211.4360 [math.NA]
- A Posteriori Error Analysis of hp-FEM for singularly perturbed problems reaction-diffusion equations
 J.M. Melenk, T. Wihler
 ASC Report 25/2014 (PDF) or at arXiv:1408.6037[math.NA]
Skripten
- A first course in Numerical Analysis (250pp)
 bitte fragen Sie nach einer Kopie
- FEM
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- Numerical methods for ODEs (100pp)
 bitte fragen Sie nach einer Kopie