Rellich-type discrete compactness for some discontinuous Galerkin FEM

DOI10.1007/s13160-012-0057-1zbMath1258.65098OpenAlexW2166587858MaRDI QIDQ691990

Fumio Kikuchi

Publication date: 4 December 2012

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://econpapers.repec.org/RePEc:hit:econdp:2011-04

zbMATH Keywords

stabilityPoisson equationdiscontinuous Galerkin finite element methodspolygonal elementRellich's theoremHilbert space methodsKolmogorov-Riesz compactness theoremdiscrete Poincaré-Friedrichs inequalities

Mathematics Subject Classification ID

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) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Convergence to weak solutions of a space-time hybridized discontinuous Galerkin method for the incompressible Navier–Stokes equations ⋮ On volumetric locking in a hybrid symmetric interior penalty method for nearly incompressible linear elasticity on polygonal meshes ⋮ A hybridized discontinuous Galerkin method with reduced stabilization ⋮ A Unified Error Analysis of Hybridizable Discontinuous Galerkin Methods for the Static Maxwell Equations ⋮ Strong $L^p$ convergence associated with Rellich-type discrete compactness for discontinuous Galerkin FEM

Cites Work

• The Kolmogorov-Riesz compactness theorem
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• An Interior Penalty Finite Element Method with Discontinuous Elements
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• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
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