Rate optimality of adaptive finite element methods with respect to overall computational costs

DOI10.1090/mcom/3654zbMath1468.65189arXiv2003.10785OpenAlexW3013489327MaRDI QIDQ4999467

Dirk Praetorius, Stefan Schimanko, Alexander Haberl, Gregor Gantner

Publication date: 7 July 2021

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.10785

zbMATH Keywords

adaptive mesh-refinementoptimal computational costsecond-order elliptic PDEconvergence of adaptive FEM

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Rate of convergence, degree of approximation (41A25) Complexity and performance of numerical algorithms (65Y20) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08)

Related Items

Adaptive quasi-Monte Carlo finite element methods for parametric elliptic PDEs ⋮ Inf-sup stability implies quasi-orthogonality ⋮ Optimal multilevel adaptive FEM for the Argyris element ⋮ Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs ⋮ Goal-oriented adaptive finite element methods with optimal computational complexity ⋮ A link between the steepest descent method and fixed-point iterations ⋮ Plain convergence of goal-oriented adaptive FEM ⋮ Relaxed Kačanov Scheme for the \(\boldsymbol{p}\)-Laplacian with Large Exponent ⋮ How to prove optimal convergence rates for adaptive least-squares finite element methods

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