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𝑝-robust equivalence of global continuous constrained and local discontinuous unconstrained approximation, a 𝑝-stable local commuting projector, and optimal elementwise ℎ𝑝 approximation estimates in 𝐻(^cp)
On full linear convergence and optimal complexity of adaptive FEM with inexact solver
Philipp Bringmann, Michael Feischl, Ani Miraçi, Dirk Praetorius and Julian Streitberger Computers & Mathematics with Applications 180 102 (2025) https://doi.org/10.1016/j.camwa.2024.12.013
Optimal convergence rates of an adaptive hybrid FEM-BEM method for full-space linear transmission problems
Hierarchical a posteriori error estimation of Bank–Weiser type in the FEniCS Project
Raphaël Bulle, Jack S. Hale, Alexei Lozinski, Stéphane P.A. Bordas and Franz Chouly Computers & Mathematics with Applications 131 103 (2023) https://doi.org/10.1016/j.camwa.2022.11.009
Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in
H
(div)
Alexandre Ern, Thirupathi Gudi, Iain Smears and Martin Vohralík IMA Journal of Numerical Analysis 42(2) 1023 (2022) https://doi.org/10.1093/imanum/draa103
H
1-stability of the L2-projection onto finite element spaces on adaptively refined quadrilateral meshes
On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion
Markus Faustmann, Jens Markus Melenk and Maryam Parvizi ESAIM: Mathematical Modelling and Numerical Analysis 55(2) 595 (2021) https://doi.org/10.1051/m2an/2020079
Equivalence of local-best and global-best approximations in H(curl)
Michael Feischl, Thomas Führer, Norbert Heuer, Michael Karkulik and Dirk Praetorius Archives of Computational Methods in Engineering 22(3) 309 (2015) https://doi.org/10.1007/s11831-014-9114-z
Adaptive FEM with Optimal Convergence Rates for a Certain Class of Nonsymmetric and Possibly Nonlinear Problems
Multiscale modeling in micromagnetics: Existence of solutions and numerical integration
F. Bruckner, D. Suess, M. Feischl, T. Führer, P. Goldenits, M. Page, D. Praetorius and M. Ruggeri Mathematical Models and Methods in Applied Sciences 24(13) 2627 (2014) https://doi.org/10.1142/S0218202514500328
EachH1/2–stable projection yields convergence and quasi–optimality of adaptive FEM with inhomogeneous Dirichlet data in Rd
M. Aurada, M. Feischl, J. Kemetmüller, M. Page and D. Praetorius ESAIM: Mathematical Modelling and Numerical Analysis 47(4) 1207 (2013) https://doi.org/10.1051/m2an/2013069
On 2D Newest Vertex Bisection: Optimality of Mesh-Closure and H 1-Stability of L 2-Projection