A remark on the optimality of adaptive finite element methods

DOI10.1016/j.crma.2010.11.011zbMath1209.65127OpenAlexW2122168573MaRDI QIDQ627761

Roland Becker, David M. Trujillo

Publication date: 3 March 2011

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2010.11.011

zbMATH Keywords

algorithmerror boundsadaptive finite element methodsPoisson equationmesh refinement

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Cites Work

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• A convergent adaptive finite element method with optimal complexity
• An optimally convergent adaptive mixed finite element method
• Adaptive finite element methods with convergence rates
• Optimality of a standard adaptive finite element method
• A Convergent Nonconforming Adaptive Finite Element Method with Quasi-Optimal Complexity
• Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
• Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
• The completion of locally refined simplicial partitions created by bisection
• A posteriori estimators for obstacle problems by the hypercircle method

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