hp-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs
M Innerberger, A Miraçi, D Praetorius… - ESAIM: Mathematical …, 2024 - esaim-m2an.org
In this work, we formulate and analyze a geometric multigrid method for the iterative solution
of the discrete systems arising from the finite element discretization of symmetric second …
of the discrete systems arising from the finite element discretization of symmetric second …
[PDF][PDF] Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs
We analyze a goal-oriented adaptive algorithm that aims to efficiently compute the quantity
of interest G (u⋆) with a linear goal functional G and the solution u⋆ to a general second …
of interest G (u⋆) with a linear goal functional G and the solution u⋆ to a general second …
-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs
M Innerberger, A Miraçi, D Praetorius… - arXiv preprint arXiv …, 2022 - arxiv.org
In this work, we formulate and analyze a geometric multigrid method for the iterative solution
of the discrete systems arising from the finite element discretization of symmetric second …
of the discrete systems arising from the finite element discretization of symmetric second …
Iterative solvers in adaptive FEM
P Bringmann, A Miraçi, D Praetorius - arXiv preprint arXiv:2404.07126, 2024 - arxiv.org
This chapter provides an overview of state-of-the-art adaptive finite element methods
(AFEMs) for the numerical solution of second-order elliptic partial differential equations …
(AFEMs) for the numerical solution of second-order elliptic partial differential equations …
Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs
We consider scalar semilinear elliptic PDEs, where the nonlinearity is strongly monotone,
but only locally Lipschitz continuous. To linearize the arising discrete nonlinear problem, we …
but only locally Lipschitz continuous. To linearize the arising discrete nonlinear problem, we …
Optimal complexity of standard and goal-oriented adaptive FEM for general second-order linear elliptic PDEs
J Streitberger - 2024 - repositum.tuwien.at
Adaptive finite element methods (AFEMs) have become an indispensable tool for efficient
numerical simulations of partial differential equations (PDEs). Such methods successfully …
numerical simulations of partial differential equations (PDEs). Such methods successfully …
On optimal adaptivity in nonlinear problems
M Brunner - 2024 - repositum.tuwien.at
This thesis is devoted to rate-optimal adaptive finite element methods (AFEMs) for
semilinear elliptic partial differential equations (PDEs). It considers a model problem with a …
semilinear elliptic partial differential equations (PDEs). It considers a model problem with a …