Exponential convergence of the \(hp\)-DGFEM for diffusion problems
type: Item
instance of: scholarly article
title: Exponential convergence of the \(hp\)-DGFEM for diffusion problems
zbMATH Open document ID: 1059.65095
DOI: 10.1016/S0898-1221(03)90088-5
author: Thomas P. Wihler
author: Philipp Frauenfelder
author: Christoph Schwab
publication date: 2004-08-06T00:00:00Z
review text: Two different formulations of the \(hp\)-discontinuous Galerkin finite element method (DGFEM) are considered for the two-dimensional stationary diffusion problem. As in the usual FEM, mesh refinement strategy is important when corner singularity caused by polygonal shape of domains exists. The authors prove exponential convergence of the \(hp\)-version of DGFEM on geometrically refined meshes in polygons. Several variants of interior penalization are covered. Numerical experiments indicate the sharpness of the theoretical results as well as the weak dependence of the DGFEM approximation on the particular choice of interior penalization and the penalty parameter. In certain cases, stabilization techniques are effective.
reviewed by: Fumio Kikuchi
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 2082259
zbMATH Keywords: FEM
zbMATH Keywords: discontinuous Galerkin methods
zbMATH Keywords: exponential convergence
zbMATH Keywords: diffusion problems
zbMATH Keywords: corner singularities
zbMATH Keywords: finite element method
zbMATH Keywords: mesh refinement
zbMATH Keywords: interior penalization
zbMATH Keywords: numerical experiments
zbMATH Keywords: stabilization
MaRDI profile type: Publication
cites work: Q4109239
cites work: The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
cites work: The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
cites work: Finite element methods for linear hyperbolic problems
cites work: An Analysis of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
cites work: Local Error Estimates for a Finite Element Method for Hyperbolic and Convection-Diffusion Equations
cites work: A Note on the Convergence of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
cites work: An Optimal-Order Error Estimate for the Discontinuous Galerkin Method
cites work: Q4952245
cites work: Q4952243
cites work: An Elliptic Collocation-Finite Element Method with Interior Penalties
cites work: Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
cites work: A discontinuous \(hp\) finite element method for diffusion problems
cites work: The Discontinuous Galerkin Method with Diffusion
cites work: Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. Part I. Boundary Value Problems for Linear Elliptic Equation of Second Order
cites work: Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. II: The Trace Spaces and Application to the Boundary Value Problems with Nonhomogeneous Boundary Conditions
cites work: Q4220650
cites work: \(hp\)-version discontinuous Galerkin methods for hyperbolic conservation laws
cites work: Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids
cites work: On the regularity of elasticity problems with piecewise analytic data
cites work: Q4490850
cites work: An hp finite element method for convection-diffusion problems in one dimension
cites work: Q2550279
cites work: Q4000182
cites work: Q4955539
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2082259