Analysis of a family of discontinuous Galerkin methods for elliptic problems: the one dimensional case

DOI10.1007/s00211-004-0528-7zbMath1064.65082OpenAlexW1972960967MaRDI QIDQ706221

A. Jonas Niklasson, Mats G. Larson

Publication date: 8 February 2005

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-004-0528-7

zbMATH Keywords

stabilityerror estimatesdiscontinuous Galerkin methodselliptic problems

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (20)

L ² -estimates for the DG IIPG-0 scheme ⋮ Pointwise error estimates and two-grid algorithms of discontinuous Galerkin method for strongly nonlinear elliptic problems ⋮ \(hp\)-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to 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 ⋮ Augmented high order finite volume element method for elliptic PDEs in non-smooth domains: Convergence study ⋮ An interior penalty discontinuous Galerkin method for a class of monotone quasilinear elliptic problems ⋮ An optimal-order \(L^2\)-error estimate for nonsymmetric discontinuous Galerkin methods for a parabolic equation in multiple space dimensions ⋮ Convergence analysis of a symmetric dual-wind discontinuous Galerkin method ⋮ The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders \(p \geqslant 2\) ⋮ Symmetric and non-symmetric discontinuous Galerkin methods stabilized using bubble enrichment ⋮ \(hp\)-discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems ⋮ On the algorithmic and implementational aspects of a discontinuous Galerkin method at finite strains ⋮ A Sequential Least Squares Method for Poisson Equation Using a Patch Reconstructed Space ⋮ Convergence analysis of symmetric dual-wind discontinuous Galerkin approximation methods for the obstacle problem ⋮ On \(L^2\)-error estimate for nonsymmetric interior penalty Galerkin approximation to linear elliptic problems with nonhomogeneous Dirichlet data ⋮ Discontinuous Galerkin finite volume element methods for second-order linear elliptic problems ⋮ Interior penalty discontinuous Galerkin methods with implicit time-integration techniques for nonlinear parabolic equations ⋮ Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension ⋮ An unfitted finite element method by direct extension for elliptic problems on domains with curved boundaries and interfaces

Cites Work

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• A discontinuous \(hp\) finite element method for diffusion problems
• A discontinuous \(hp\) finite element method for diffusion problems: 1-D analysis
• Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
• An Interior Penalty Finite Element Method with Discontinuous Elements
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• 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

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