The \(hp\)-adaptive FEM based on continuous Sobolev embeddings: isotropic refinements

DOI10.1016/j.camwa.2013.05.024zbMath1416.65443OpenAlexW1979928109MaRDI QIDQ316568

Thomas Fankhauser, Marcel Wirz, Thomas P. Wihler

Publication date: 27 September 2016

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2013.05.024

zbMATH Keywords

Sobolev embeddings\(hp\)-adaptivity\(hp\)-FEM

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items

An $hp$-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems, Editorial: High-order finite element approximation for partial differential equations, An h p -adaptive Newton-Galerkin finite element procedure for semilinear boundary value problems, A general finite element method: extension of variational analysis for nonlinear heat conduction with temperature-dependent properties and boundary conditions, and its implementation as local refinement, \(hp\)-adaptive Galerkin time stepping methods for nonlinear initial value problems, $hp$-Adaptation Driven by Polynomial-Degree-Robust A Posteriori Error Estimates for Elliptic Problems

Uses Software

• deal.ii

Cites Work

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• An \(hp\)-adaptive strategy based on continuous Sobolev embeddings
• Toward a universal h-p adaptive finite element strategy. III: Design of h-p meshes
• An adaptive strategy for \(hp\)-FEM based on testing for analyticity
• The h-p version of the finite element method. I. The basic approximation results
• The h-p version of the finite element method. II. General results and applications
• Approximation properties of the \(h\)-\(p\) version of the finite element method
• An adaptive refinement strategy for \(hp\)-finite element computations
• A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations
• The h, p and h-p versions of the finite element method in 1 dimension. II. The error analysis of the h- and h-p versions
• Adaptive mesh strategies for the spectral element method
• Convergence of an adaptive \( hp\) finite element strategy in one space dimension
• $hp$-dGFEM for Second-Order Elliptic Problems in Polyhedra I: Stability on Geometric Meshes
• $hp$-DGFEM for Second Order Elliptic Problems in Polyhedra II: Exponential Convergence
• Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ³, Part I: countably normed spaces on polyhedral domains
• Evaluation of the Least Constant in Sobolev’s Inequality for $H^1 (0,s)$
• deal.II—A general-purpose object-oriented finite element library
• Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. Part I. Boundary Value Problems for Linear Elliptic Equation of Second Order
• Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ³. Part II: Regularity in neighbourhoods of edges
• Sobolev regularity estimation for hp-adaptive finite element methods
• THE HP-VERSION OF THE STREAMLINE DIFFUSION FINITE ELEMENT METHOD IN TWO SPACE DIMENSIONS
• Computing with hp-ADAPTIVE FINITE ELEMENTS
• On residual-based a posteriori error estimation in hp-FEM