Estimation of penalty parameters for symmetric interior penalty Galerkin methods

Authors:
Yekaterina Epshteyn;Béatrice Rivière
Affiliations:
Department of Mathematics, University of Pittsburgh, 301 Thackeray, Pittsburgh, PA 15260, USA;Department of Mathematics, University of Pittsburgh, 301 Thackeray, Pittsburgh, PA 15260, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 9
Cited 7

Piecewise solenoidal vector fields and the Stokes problem

SIAM Journal on Numerical Analysis
A Nonconforming Finite Element Method for the Stationary Navier--Stokes Equations

SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems
Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems

SIAM Journal on Numerical Analysis
A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems

SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

SIAM Journal on Numerical Analysis
Locally Conservative Coupling of Stokes and Darcy Flows

SIAM Journal on Numerical Analysis
Symmetric and Nonsymmetric Discontinuous Galerkin Methods for Reactive Transport in Porous Media

SIAM Journal on Numerical Analysis
A Discontinuous Subgrid Eddy Viscosity Method for the Time-Dependent Navier--Stokes Equations

SIAM Journal on Numerical Analysis

Discontinuous Galerkin methods for the chemotaxis and haptotaxis models

Journal of Computational and Applied Mathematics
Analysis of hp discontinuous Galerkin methods for incompressible two-phase flow

Journal of Computational and Applied Mathematics
Efficient computable error bounds for discontinuous Galerkin approximations of elliptic problems

Journal of Computational and Applied Mathematics
Primal Discontinuous Galerkin Methods for Time-Dependent Coupled Surface and Subsurface Flow

Journal of Scientific Computing
Fully Computable Error Bounds for Discontinuous Galerkin Finite Element Approximations on Meshes with an Arbitrary Number of Levels of Hanging Nodes

SIAM Journal on Numerical Analysis
Compact and Stable Discontinuous Galerkin Methods for Convection-Diffusion Problems

SIAM Journal on Scientific Computing
On the stability of the symmetric interior penalty method for the Spalart-Allmaras turbulence model

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.30

Visualization

Abstract

This paper presents computable lower bounds of the penalty parameters for stable and convergent symmetric interior penalty Galerkin methods. In particular, we derive the explicit dependence of the coercivity constants with respect to the polynomial degree and the angles of the mesh elements. Numerical examples in all dimensions and for different polynomial degrees are presented. We show the numerical effects of loss of coercivity.