Higher Order BEM-Based FEM on Polygonal Meshes

DOI10.1137/110849481zbMath1264.65196OpenAlexW1991812987MaRDI QIDQ4903761

Steffen Weißer, Sergej Rjasanow

Publication date: 24 January 2013

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/809284fff966570a451d6959b385d713c076bc3a

zbMATH Keywords

numerical experimentsconforming finite element methodconvergence orderhigher-order schemepolygonal meshboundary element method (BEM)BEM-based evaluationlocally defined trial functions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (41)

Non-conforming harmonic virtual element method: \(h\)- and \(p\)-versions ⋮ Arbitrary order Trefftz-like basis functions on polygonal meshes and realization in BEM-based FEM ⋮ Virtual element methods for parabolic problems on polygonal meshes ⋮ CVEM-BEM coupling with decoupled orders for 2D exterior Poisson problems ⋮ A High-Order Method for Evaluating Derivatives of Harmonic Functions in Planar Domains ⋮ A posteriori error estimates for a virtual element method for the Steklov eigenvalue problem ⋮ The virtual element method in 50 lines of MATLAB ⋮ A multigrid algorithm for the p-version of the virtual element method ⋮ Exponential convergence of the \(hp\) virtual element method in presence of corner singularities ⋮ The dual-weighted residual estimator realized on polygonal meshes ⋮ Convection-adapted BEM-based FEM ⋮ \( \boldsymbol{H}^1\)-conforming virtual element method for the Laplacian eigenvalue problem in mixed form ⋮ An H1-conforming virtual element for Darcy and Brinkman equations ⋮ Weak Galerkin finite element with curved edges ⋮ BDDC and FETI-DP for the virtual element method ⋮ Trefftz Finite Elements on Curvilinear Polygons ⋮ Static Condensation, Hybridization, and the Devising of the HDG Methods ⋮ FETI-DP for the Three Dimensional Virtual Element Method ⋮ Mixed FEM for Second Order Elliptic Problems on Polygonal Meshes with BEM-Based Spaces ⋮ Recovered finite element methods on polygonal and polyhedral meshes ⋮ Recovery-based error estimators for the VEM and BEM-based FEM ⋮ A brief review on polygonal/polyhedral finite element methods ⋮ Ill‐conditioning in the virtual element method: Stabilizations and bases ⋮ Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons ⋮ A Fully Computable A Posteriori Error Estimate for the Stokes Equations on Polytopal Meshes ⋮ A simple and effective gradient recovery scheme and \textit{a posteriori} error estimator for the virtual element method (VEM) ⋮ A nonconforming Trefftz virtual element method for the Helmholtz problem: numerical aspects ⋮ FEM with Trefftz trial functions on polyhedral elements ⋮ A Nyström-based finite element method on polygonal elements ⋮ The Hitchhiker's Guide to the Virtual Element Method ⋮ New perspectives on polygonal and polyhedral finite element methods ⋮ Addressing integration error for polygonal finite elements through polynomial projections: A patch test connection ⋮ Residual based error estimate and quasi-interpolation on polygonal meshes for high order BEM-based FEM ⋮ Virtual elements for a shear-deflection formulation of Reissner–Mindlin plates ⋮ Error estimation for the polygonal finite element method for smooth and singular linear elasticity ⋮ A virtual element method for the Steklov eigenvalue problem allowing small edges ⋮ A stress/displacement virtual element method for plane elasticity problems ⋮ Anisotropic polygonal and polyhedral discretizations in finite element analysis ⋮ A posteriori error estimation and adaptivity in \textit{hp} virtual elements ⋮ Quadrature for implicitly-defined finite element functions on curvilinear polygons ⋮ A Family of $H(div)$ Finite Element Approximations on Polygonal Meshes

This page was built for publication: Higher Order BEM-Based FEM on Polygonal Meshes