Some nonstandard error analysis of discontinuous Galerkin methods for elliptic problems

DOI10.1007/s10092-010-0022-9zbMath1214.65058OpenAlexW2110061249MaRDI QIDQ607692

Thirupathi Gudi

Publication date: 3 December 2010

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10092-010-0022-9

zbMATH Keywords

stabilitydiscontinuous Galerkin methodunicitya priori error estimateselliptic boundary value problemGarding type inequality

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)

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Cites Work

• \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
• Two-level non-overlapping Schwarz preconditioners for a discontinuous Galerkin approximation of the biharmonic equation
• Mixed discontinuous Galerkin finite element method for the biharmonic equation
• Sub-optimal convergence of non-symmetric discontinuous Galerkin methods for odd polynomial approximations
• The \(L^{2}\)-optimality of the IIPG method for odd degrees of polynomial approximation in 1D
• A weakly over-penalized symmetric interior penalty method
• \(hp\)-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation
• A posteriori error estimation and adaptive mesh-refinement techniques
• An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
• A new error analysis for discontinuous finite element methods for linear elliptic problems
• ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS
• Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems
• Singularities of Maxwell interface problems
• An Interior Penalty Finite Element Method with Discontinuous Elements
• Finite Element Methods for Elliptic Equations Using Nonconforming Elements
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Poincaré--Friedrichs Inequalities for Piecewise H¹ Functions
• A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
• A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Minimal regularity of the solutions of some transmission problems
• The Mathematical Theory of Finite Element Methods
• Discontinuous Galerkin Methods for Quasi‐Linear Elliptic Problems of Nonmonotone Type
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