• Numerische Lösung von PDEs

  • Least-Squares-Finite-Elemente-Methoden

  • adaptive Netzverfeinerung

  • diskontinuierliche Petrov-Galerkin-Methoden

  • nichtkonforme Methoden

  • Anwendungen in der Mechanik

  1. P. Bringmann, J. W. Ketteler, M. Schedensack. Discrete Helmholtz decompositions of piecewise constant and piecewise affine vector and tensor fields, Found. Comput. Math., online veröffentlicht, 2024. [doi:10.1007/s10208-024-09642-1]
  2. P. Bringmann, C. Carstensen, J. Streitberger. Local parameter selection in the C0 interior penalty method for the biharmonic equation. J. Numer. Math., online veröffentlicht, 2023. [doi:10.1515/jnma-2023-0028]
  3. P. Bringmann. How to prove optimal convergence rates for adaptive least-squares finite element methods. J. Numer. Math. 31(1): 43–58, 2023. [doi:10.1515/jnma-2021-0116]
  4. P. Bringmann, C. Carstensen, N. T. Tran. Adaptive least-squares, discontinuous Petrov-Galerkin, and hybrid high-order methods. In: Schröder, J., Wriggers, P. (Ed.) Non-standard Discretisation Methods in Solid Mechanics. Lecture Notes in Applied and Computational Mechanics, Vol. 98. Springer, Cham, 2022. [doi:10.1007/978-3-030-92672-4_5]
  5. P. Bringmann, C. Carstensen, G. Starke. An adaptive least-squares FEM for linear elasticity with optimal convergence rates. SIAM J. Numer. Anal. 56(1): 428–447, 2018. [doi:10.1137/16M1083797]
  6. C. Carstensen, P. Bringmann, F. Hellwig, P. Wriggers. Nonlinear discontinuous Petrov-Galerkin methods. Numer. Math. 139: 529–561, 2018. [doi:10.1007/s00211-018-0947-5]
  7. P. Bringmann, C. Carstensen. h-adaptive least-squares finite element methods for the 2D Stokes equations of any order with optimal convergence rates. Comput. Math. Appl. 74(8): 1923–1939, 2017. [doi:10.1016/j.camwa.2017.02.019]
  8. P. Bringmann, C. Carstensen. An adaptive least-squares FEM for the Stokes equations with optimal convergence rates. Numer. Math. 135: 459–492, 2017. [doi:10.1007/s00211-016-0806-1]
  9. C. Carstensen, E. J. Park, P. Bringmann. Convergence of natural adaptive least squares FEMs. Numer. Math. 136: 1097–1115, 2017. [doi:10.1007/s00211-017-0866-x]
  10. P. Bringmann, C. Carstensen, C. Merdon. Guaranteed velocity error control for the pseudo-stress approximation of the Stokes equations. Numer. Methods Partial Differential Eqs 32: 1411-1432, 2016. [doi:10.1002/num.22056]
  11. P. Bringmann, C. Carstensen, D. Gallistl, F. Hellwig, D. Peterseim, S. Puttkammer, H. Rabus, J. Storn. Towards adaptive discontinuous Petrov-Galerkin methods. Proc. Appl. Math. Mech. 16: 741-742, 2016. [doi:10.1002/pamm.201610359]

  1. P. Bringmann, M. Brunner, D. Praetorius, J. Streitberger. Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs, 2023. [arxiv:2312.00489]
  2. P. Bringmann, M. Feischl, A. Miraçi, D. Praetorius, J. Streitberger. On full linear convergence and optimal complexity of adaptive FEM with inexact solver, 2023. [arxiv:2311.15738]
  3. P. Bringmann. Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods, 2023, [arxiv:2310.19930]
  4. P. Bringmann. Review and computational comparison of adaptive least-squares finite element schemes, 2023. [arxiv:2209.06028]