My research focuses on three main areas

• Partial differential equations with random coefficients, fast random field generation, and machine learning
• Computational micromagnetism as well as numerics and theory of the Landau-Lifshitz-Gilbert equation
• Optimal adaptive mesh refinement and a posteriori error estimators

ERC-Consolidator Project: "New Frontiers in Optimal Adaptivity" 

Lecturenotes to all of my courses can be found under

https://michaelfeischl.github.io/lecturenotes/, opens an external URL in a new window

• Wavelet compression for sampling deep Gaussian processes.
  O. Broukal, M. Feischl, and C. Osborne.
  arXiv E-print, 2026.
• High Probability Derivative Bounds for Random tanh Neural Networks on a Hypercube.
  J. Dick, M. Feischl, and F. Zehetgruber.
  arXiv E-print, 2026.
• BDF2-type integrator for Landau–Lifshitz–Gilbert equation in micromagnetics: a-priori error estimates.
  M. Aldé, M. Feischl, and D. Praetorius.
  arXiv E-print, 2026.
• BDF2-type integrator for Landau–Lifshitz–Gilbert equation in micromagnetics: Unconditional weak convergence to weak solutions.
  M. Aldé, M. Feischl, and D. Praetorius.
  In Math. Comp., published online, 2026. arXiv E-print.
• Regularized dynamical parametric approximation.
  M. Feischl, C. Lasser, C. Lubich, and J. Nick.
  In Numer. Math., 158: 2079–2123, 2026. arXiv E-print.
• Optimal Time-Adaptivity for Parabolic Problems.
  M. Feischl, F. Henríquez, and D. Niederkofler.
  arXiv E-print, 2025.
• A Reduced Basis Method for the Stochastic Landau–Lifshitz–Gilbert Equation.
  A. Scaglioni, M. Feischl, and F. Henríquez.
  arXiv E-print, 2025.
• Optimal adaptive implicit time stepping.
  M. Feischl and D. Niederkofler.
  In Advances in Applied Mechanics, 61: 407–448, 2025. arXiv E-print.
• Computational Math with Neural Networks is Hard.
  M. Feischl, B. Grässle, and F. Zehetgruber.
  arXiv E-print, 2025.
• Well-Posedness of Discretizations for Fractional Elasto-Plasticity.
  M. Feischl, D. Niederkofler, and B. Wohlmuth.
  arXiv E-print, 2025.
• Neural General Operator Networks via Banach Fixed Point Iterations.
  M. Feischl, C. Schwab, and F. Zehetgruber.
  SAM Research Report, no. 2025-13, 2025. Accepted in Mathematical Foundations of Machine Learning.
• Sparse Grid Approximation of Nonlinear SPDEs: The Landau–Lifshitz–Gilbert Equation.
  X. An, J. Dick, M. Feischl, A. Scaglioni, and T. Tran.
  In SIAM/ASA J. Uncertain. Quantification, 13 (2): 472–517, 2025. arXiv E-print.
• On full linear convergence and optimal complexity of adaptive FEM with inexact solver.
  P. Bringmann, M. Feischl, A. Miraçi, D. Praetorius, and J. Streitberger.
  In Comput. Math. Appl., 180: 102–129, 2025. arXiv E-print.
• Towards optimal hierarchical training of neural networks.
  M. Feischl, A. Rieder, and F. Zehetgruber.
  arXiv E-print, 2024.
• Adaptive Image Compression via Optimal Mesh Refinement.
  M. Feischl and H. Hackl.
  In Comput. Methods Appl. Math., 24 (2): 325–343, 2024. arXiv E-print.
• Adaptive mesh refinement for the Landau–Lifshitz–Gilbert equation.
  J. Bohn, W. Dörfler, M. Feischl, and S. Karch.
  arXiv E-print, 2023.
• FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation.
  J. Bohn, M. Feischl, and B. Kovács.
  In Comput. Methods Appl. Math., 23 (1): 19–48, 2023.
• Inf-sup stability implies quasi-orthogonality.
  M. Feischl.
  In Math. Comp., 91 (337): 2059–2094, 2022.
• Low-entry-barrier point-of-care testing of anti-SARS-CoV-2 IgG in the population of Upper Austria from December 2020 until April 2021 - a feasible surveillance strategy for post-pandemic monitoring?
  C. Doppler, M. Feischl, C. Ganhör, S. Puh, M. Müller, M. Kotnik, T. Mimler, M. Sonnleitner, D. Bernhard, and C. Wechselberger.
  In Anal. Bioanal. Chem., 414 (10): 3291–3299, 2022.
• Convergence of adaptive stochastic collocation with finite elements.
  M. Feischl and A. Scaglioni.
  In Comput. Math. Appl., 98: 139–156, 2021. DOI.
• Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation.
  G. Akrivis, M. Feischl, B. Kovács, and C. Lubich.
  In Math. Comp., 90 (329): 995–1038, 2021.
• Recurrent neural networks as optimal mesh refinement strategies.
  J. Bohn and M. Feischl.
  In Comput. Math. Appl., 97: 61–76, 2021.
• A quasi-Monte Carlo data compression algorithm for machine learning.
  J. Dick and M. Feischl.
  In J. Complexity, 67: 101587, 2021. DOI.
• Exponential convergence in $H^1$ of $hp$-FEM for Gevrey regularity with isotropic singularities.
  M. Feischl and C. Schwab.
  In Numer. Math., 144 (2): 323–346, 2020.
• Sparse compression of expected solution operators.
  M. Feischl and D. Peterseim.
  In SIAM J. Numer. Anal., 58 (6): 3144–3164, 2020.
• Optimality of a standard adaptive finite element method for the Stokes problem.
  M. Feischl.
  In SIAM J. Numer. Anal., 57 (3): 1124–1157, 2019.
• Improved efficiency of a multi-index FEM for computational uncertainty quantification.
  J. Dick, M. Feischl, and C. Schwab.
  In SIAM J. Numer. Anal., 57 (4): 1744–1769, 2019.
• Fast random field generation with H-matrices.
  M. Feischl, F. Y. Kuo, and I. H. Sloan.
  In Numer. Math., 140 (3): 639–676, 2018.
• Optimal adaptivity for non-symmetric FEM/BEM coupling.
  M. Feischl.
  arXiv E-print, 2017.
• Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations.
  M. Feischl, G. Gantner, A. Haberl, and D. Praetorius.
  In Numer. Math., 136 (1): 147–182, 2017.
• Local inverse estimates for non-local boundary integral operators.
  M. Aurada, M. Feischl, T. Führer, M. Karkulik, J. M. Melenk, and D. Praetorius.
  In Math. Comp., 86 (308): 2651–2686, 2017.
• The Eddy Current–LLG Equations: FEM-BEM Coupling and A Priori Error Estimates.
  M. Feischl and T. Tran.
  In SIAM J. Numer. Anal., 55 (4): 1786–1819, 2017.
• Existence of regular solutions of the Landau–Lifshitz–Gilbert equation in 3D with natural boundary conditions.
  M. Feischl and T. Tran.
  In SIAM J. Math. Anal., 49 (6): 4470–4490, 2017.
• Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations.
  M. Feischl, T. Führer, D. Praetorius, and E. P. Stephan.
  In Calcolo, 54 (1): 367–399, 2017.
• Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements.
  M. Feischl, T. Führer, D. Praetorius, and E. P. Stephan.
  In Numer. Methods Partial Differential Equations, 33 (3): 603–632, 2017.
• Adaptive 2D IGA boundary element methods.
  M. Feischl, G. Gantner, A. Haberl, and D. Praetorius.
  In Eng. Anal. Bound. Elem., 62: 141–153, 2016.
• An abstract analysis of optimal goal-oriented adaptivity.
  M. Feischl, D. Praetorius, and K. G. van der Zee.
  In SIAM J. Numer. Anal., 54 (3): 1423–1448, 2016.
• Efficient numerical computation of direct exchange areas in thermal radiation analysis.
  M. Feischl, T. Führer, M. Niederer, S. Strommer, A. Steinboeck, and D. Praetorius.
  In Numerical Heat Transfer, Part B: Fundamentals, 69 (6): 511–533, 2016.
• Adaptive boundary element methods for optimal convergence of point errors.
  M. Feischl, G. Gantner, A. Haberl, D. Praetorius, and T. Führer.
  In Numer. Math., 132 (3): 541–567, 2016.
• Energy norm based error estimators for adaptive BEM for hypersingular integral equations.
  M. Aurada, M. Feischl, T. Führer, M. Karkulik, and D. Praetorius.
  In Appl. Numer. Math., 95: 15–35, 2015.
• Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. Part II: Hyper-singular integral equation.
  M. Feischl, T. Führer, M. Karkulik, J. M. Melenk, and D. Praetorius.
  In Electron. Trans. Numer. Anal., 44: 153–176, 2015.
• Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations.
  M. Feischl, G. Gantner, and D. Praetorius.
  In Comput. Methods Appl. Mech. Engrg., 290: 362–386, 2015.
• Stability of symmetric and nonsymmetric FEM-BEM couplings for nonlinear elasticity problems.
  M. Feischl, T. Führer, M. Karkulik, and D. Praetorius.
  In Numer. Math., 130 (2): 199–223, 2015.
• Adaptive Boundary Element Methods: A Posteriori Error Estimators, Adaptivity, Convergence, and Implementation.
  M. Feischl, T. Führer, N. Heuer, M. Karkulik, and D. Praetorius.
  In Arch. Comput. Methods Eng., 22 (3): 309–389, 2015.
• Multiscale modeling in micromagnetics: Existence of solutions and numerical integration.
  F. Bruckner, D. Süss, M. Feischl, T. Führer, P. Goldenits, M. Page, D. Praetorius, and M. Ruggeri.
  In Math. Models Methods Appl. Sci., 24 (13): 2627–2662, 2014.
• Axioms of adaptivity.
  C. Carstensen, M. Feischl, M. Page, and D. Praetorius.
  In Comput. Math. Appl., 67 (6): 1195–1253, 2014.
• Adaptive FEM with optimal convergence rates for a certain class of nonsymmetric and possibly nonlinear problems.
  M. Feischl, T. Führer, and D. Praetorius.
  In SIAM J. Numer. Anal., 52 (2): 601–625, 2014.
• Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data.
  M. Feischl, M. Page, and D. Praetorius.
  In J. Comput. Appl. Math., 255: 481–501, 2014.
• Convergence of adaptive FEM for some elliptic obstacle problem with inhomogeneous Dirichlet data.
  M. Feischl, M. Page, and D. Praetorius.
  In Int. J. Numer. Anal. Model., 11 (1): 229–253, 2014.
• Convergence of adaptive BEM and adaptive FEM-BEM coupling for estimators without h-weighting factor.
  M. Feischl, T. Führer, G. Mitscha-Eibl, D. Praetorius, and E. P. Stephan.
  In Comput. Methods Appl. Math., 14 (4): 485–508, 2014.
• ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve.
  M. Feischl, T. Führer, M. Karkulik, and D. Praetorius.
  In Eng. Anal. Bound. Elem., 38: 49–60, 2014.
• HILBERT — a MATLAB implementation of adaptive 2D-BEM.
  M. Aurada, M. Ebner, M. Feischl, S. Ferraz-Leite, T. Führer, P. Goldenits, M. Karkulik, M. Mayr, and D. Praetorius.
  In Numer. Algorithms, 67 (1): 1–32, 2014.
• Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, Part I: weakly-singular integral equation.
  M. Feischl, T. Führer, M. Karkulik, J. M. Melenk, and D. Praetorius.
  In Calcolo, 51 (4): 531–562, 2014.
• Classical FEM-BEM coupling methods: Nonlinearities, well-posedness, and adaptivity.
  M. Aurada, M. Feischl, T. Führer, M. Karkulik, J. M. Melenk, and D. Praetorius.
  In Comput. Mech., 51 (4): 399–419, 2013.
• Each $H^{1/2}$-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in $\mathbb{R}^d$.
  M. Aurada, M. Feischl, J. Kemetmüller, M. Page, and D. Praetorius.
  In ESAIM Math. Model. Numer. Anal., 47 (4): 1207–1235, 2013.
• Efficiency and optimality of some weighted-residual error estimator for adaptive 2D boundary element methods.
  M. Aurada, M. Feischl, T. Führer, M. Karkulik, and D. Praetorius.
  In Comput. Methods Appl. Math., 13 (3): 305–332, 2013.
• Combining micromagnetism and magnetostatic Maxwell equations for multiscale magnetic simulations.
  F. Bruckner, C. Vogler, B. Bergmair, T. Huber, M. Fuger, D. Süss, M. Feischl, T. Führer, M. Page, and D. Praetorius.
  In J. Magn. Magn. Mater., 343: 163–168, 2013.
• Quasi-optimal convergence rate for an adaptive boundary element method.
  M. Feischl, M. Karkulik, J. M. Melenk, and D. Praetorius.
  In SIAM J. Numer. Anal., 51 (2): 1327–1348, 2013.
• A posteriori error estimates for the Johnson–Nédélec FEM-BEM coupling.
  M. Aurada, M. Feischl, M. Karkulik, and D. Praetorius.
  In Eng. Anal. Bound. Elem., 36 (2): 255–266, 2012.
• Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems.
  M. Aurada, M. Feischl, and D. Praetorius.
  In ESAIM Math. Model. Numer. Anal., 46 (5): 1147–1173, 2012.
• 3D FEM-BEM-coupling method to solve magnetostatic Maxwell equations.
  F. Bruckner, C. Vogler, M. Feischl, D. Praetorius, B. Bergmair, T. Huber, M. Fuger, and D. Süss.
  In J. Magn. Magn. Mater., 324: 1862–1866, 2012.