L 2 error estimates for a nonstandard finite element method on polyhedral meshes

DOI10.1515/JNUM.2011.002zbMath1222.65119OpenAlexW2107205741MaRDI QIDQ3006387

Clemens Hofreither

Publication date: 14 June 2011

Published in: Journal of Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jnum.2011.002

zbMATH Keywords

error estimatesboundary element methodmixed formulationpolyhedral meshesBEM-based FEM

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (13)

Arbitrary order Trefftz-like basis functions on polygonal meshes and realization in BEM-based FEM ⋮ A High-Order Method for Evaluating Derivatives of Harmonic Functions in Planar Domains ⋮ Convection-adapted BEM-based FEM ⋮ Evaluation of Inner Products of Implicitly Defined Finite Element Functions on Multiply Connected Planar Mesh Cells ⋮ Trefftz Finite Elements on Curvilinear Polygons ⋮ A Rigorous Error Analysis of Coupled FEM-BEM Problems with Arbitrary Many Subdomains ⋮ FEM with Trefftz trial functions on polyhedral elements ⋮ A Nyström-based finite element method on polygonal elements ⋮ Residual based error estimate and quasi-interpolation on polygonal meshes for high order BEM-based FEM ⋮ Error estimation for the polygonal finite element method for smooth and singular linear elasticity ⋮ Quadrature for implicitly-defined finite element functions on curvilinear polygons ⋮ Shape-explicit constants for some boundary integral operators ⋮ FETI Solvers for Non-standard Finite Element Equations Based on Boundary Integral Operators

Cites Work

• Quasiconformal mappings and extendability of functions in Sobolev spaces
• A note on the Poincaré inequality for convex domains
• The mimetic finite difference method on polygonal meshes for diffusion-type problems
• Analysis of the discontinuous Galerkin method for nonlinear convection--diffusion problems
• Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
• Mixed finite element method for diffusion equations on polygonal meshes with mixed cells

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