Residual based error estimate and quasi-interpolation on polygonal meshes for high order BEM-based FEM

DOI10.1016/j.camwa.2016.11.013zbMath1368.65238arXiv1511.08993OpenAlexW2270650927MaRDI QIDQ2013800

Steffen Weißer

Publication date: 9 August 2017

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

Full work available at URL: https://arxiv.org/abs/1511.08993

zbMATH Keywords

quasi-interpolationpolygonal finite elementsPoincaré constantBEM-based FEMresidual based error estimate

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) Boundary element methods for boundary value problems involving PDEs (65N38)

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Cites Work

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• Arbitrary order Trefftz-like basis functions on polygonal meshes and realization in BEM-based FEM
• A posteriori error estimates for weak Galerkin finite element methods for second order elliptic problems
• Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons
• Analysis of a non-standard finite element method based on boundary integral operators
• Residual error estimate for BEM-based FEM on polygonal meshes
• An optimal Poincaré inequality for convex domains
• On the solution of the inhomogeneous polyharmonic equation and the inhomogeneous Helmholtz equation
• A posteriori error estimates for the virtual element method
• FEM with Trefftz trial functions on polyhedral elements
• Analysis of the discontinuous Galerkin method for nonlinear convection--diffusion problems
• The mimetic finite difference method for elliptic problems
• L 2 error estimates for a nonstandard finite element method on polyhedral meshes
• Arbitrary-Order Nodal Mimetic Discretizations of Elliptic Problems on Polygonal Meshes
• Poincare constants for finite element stars
• A weak Galerkin mixed finite element method for second order elliptic problems
• From the Boundary Element Domain Decomposition Methods to Local Trefftz Finite Element Methods on Polyhedral Meshes
• Polynomial Approximation of Functions in Sobolev Spaces
• A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Higher Order BEM-Based FEM on Polygonal Meshes
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• Hierarchical A Posteriori Error Estimators for the Mimetic Discretization of Elliptic Problems
• Mixed FEM for Second Order Elliptic Problems on Polygonal Meshes with BEM-Based Spaces
• Residuala posteriorierror estimation for the Virtual Element Method for elliptic problems
• Residual Based Error Estimate for Higher Order Trefftz-Like Trial Functions on Adaptively Refined Polygonal Meshes
• Equivalent Norms for Sobolev Spaces