Adaptive refinement based on asymptotic expansions of finite element solutions for node insertion in 1d

DOI10.1002/gamm.201210012zbMath1266.65190OpenAlexW2068826791MaRDI QIDQ4900444

Jan Friederich, Paul Steinmann, Günter R. Leugering

Publication date: 24 January 2013

Published in: GAMM-Mitteilungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/gamm.201210012

zbMATH Keywords

numerical examplefinite elementPoisson equationmesh optimizationerror estimatoradaptive refinementrefinement indicator

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) 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) 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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• An optimal triangulation for second-order elliptic problems
• Topological sensitivity analysis
• Topological derivatives for networks of elastic strings
• A‐posteriori error estimates for the finite element method

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