Domain Decomposition and hp-Adaptive Finite Elements

DOI10.1007/978-3-642-11304-8_1zbMath1217.65217OpenAlexW198847271MaRDI QIDQ2998401

Randolph E. Bank, Hieu Nguyen

Publication date: 18 May 2011

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-11304-8_1

zbMATH Keywords

numerical examplesdomain decompositionsuperconvergencea posteriori error estimatesresearch surveyPoisson equation\(hp\)-adaptive finite element methodhigh order finite elements

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) 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) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

On the convergence of an optimal additive Schwarz method for parallel adaptive finite elements, \(hp\) adaptive finite elements based on derivative recovery and superconvergence, An optimal Schwarz preconditioner for a class of parallel adaptive finite elements

Cites Work

• A New Paradigm for Parallel Adaptive Meshing Algorithms
• Superconvergent Derivative Recovery for Lagrange Triangular Elements of Degreepon Unstructured Grids
• A New Paradigm for Parallel Adaptive Meshing Algorithms
• Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence
• Asymptotically Exact A Posteriori Error Estimators, Part II: General Unstructured Grids
• A Domain Decomposition Solver for a Parallel Adaptive Meshing Paradigm
• Convergence analysis of a domain decomposition paradigm