• Numerics of PDEs
  • Finite Element Methods
  • Multigrid methods
  • A posteriori error estimates
  • p-robustness
  • Cost-optimality of adaptive FEM

  1. M. Innerberger, A. Miraçi, D. Praetorius, J. Streitberger: hp-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs, ESAIM: Mathematical Modelling and Numerical Analysis, in print (2023). [www] [arXiv:2210.10415],  
  2. M. Brunner, P. Heid, M. Innerberger, A. Miraçi, D. Praetorius, J. Streitberger: Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs, IMA Journal of Numerical Analysis (2023). [www]  [arXiv:2212.00353]
  3. A. Miraçi, J. Papež, M. Vohralík: A-posteriori-steered p-robust multigrid with optimal step-sizes and adaptive number of smoothing steps, SIAM J. Sci. Comput. 43, 5 (2021), S117–S145. [www] [preprint]
  4. A. Miraçi, J. Papež, M. Vohralík: Contractive local adaptive smoothing based on Dörfler’s marking in a-posteriori-steered p-robust multigrid solvers, Comput. Methods Appl. Math. 21, 2 (2021), 445–468. [www] [preprint]
  5. A. Miraçi, J. Papež, M. Vohralík: A multilevel algebraic error estimator and the corresponding iterative solver with p-robust behavior, SIAM J. Numer. Anal. 58, 5 (2020), 2856–2884. [www] [preprint]

 

  1. P. Bringmann, A. Miraçi, D. Praetorius: Iterative solvers in adaptive FEM, [arXiv:2404.07126], 2024
  2. A. Miraçi, D. Praetorius, J. Streitberger: Parameter-robust full linear convergence and optimal complexity of adaptive iteratively linearized FEM for nonlinear PDEs, [arXiv:2401.17778], 2024
  3. P. Bringmann, M. Feischl, A. Miraçi, D. Praetorius, J. Streitberger: On full linear convergence and optimal complexity of adaptive FEM with inexact solver, [arXiv:2311.15738], 2023