Preconditioning of Symmetric Interior Penalty Discontinuous Galerkin FEM for Elliptic Problems

2008 ◽  
pp. 33-44 ◽  
Author(s):  
Veselin A. Dobrev ◽  
Raytcho D. Lazarov ◽  
Ludmil T. Zikatanov
Keyword(s):  
Discontinuous Galerkin ◽  
Elliptic Problems ◽  
Interior Penalty ◽  
Discontinuous Galerkin Fem

scholarly journals Interior Penalty Discontinuous Galerkin FEM for the $p(x)$-Laplacian

2012 ◽  
Vol 50 (5) ◽  
pp. 2497-2521 ◽  
Author(s):  
Leandro M. Del Pezzo ◽  
Ariel L. Lombardi ◽  
Sandra Martínez
Keyword(s):  
Discontinuous Galerkin ◽  
Interior Penalty ◽  
Discontinuous Galerkin Fem

Sharp Expressions for the Stabilization Parameters in Symmetric Interior-penalty Discontinuous Galerkin Finite Element Approximations of Fourth-order Elliptic Problems

2007 ◽  
Vol 7 (4) ◽  
pp. 365-375 ◽  
Author(s):  
I. Mozolevski ◽  
P.R. Bösing
Keyword(s):  
Finite Element ◽  
Discontinuous Galerkin ◽  
Fourth Order ◽  
Elliptic Problems ◽  
Penalty Parameter ◽  
Interior Penalty ◽  
Galerkin Finite Element ◽  
Finite Element Approximations ◽  
Discontinuous Galerkin Finite Element ◽  
Parameter Values

Abstract In this paper, we derive explicit expressions for the penalty parameters appearing in symmetric and semi-symmetric interior-penalty discontinuous Galerkin finite element method (DGFEM) for fourth-order elliptic problems. We demonstrate the sharpness of the theoretically predicted penalty parameter values through numerical experiments.

Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems

2020 ◽  
Vol 28 (3) ◽  
pp. 161-174
Author(s):  
Maurice S. Fabien ◽  
Matthew G. Knepley ◽  
Beatrice M. Riviere
Keyword(s):  
Error Estimates ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Computational Cost ◽  
Elliptic Problems ◽  
Second Order ◽  
Three Dimensions ◽  
Galerkin Methods ◽  
Interior Penalty ◽  
Second Order Elliptic Problems

AbstractThe focus of this paper is the analysis of families of hybridizable interior penalty discontinuous Galerkin methods for second order elliptic problems. We derive a priori error estimates in the energy norm that are optimal with respect to the mesh size. Suboptimal L2-norm error estimates are proven. These results are valid in two and three dimensions. Numerical results support our theoretical findings, and we illustrate the computational cost of the method.

Sign in / Sign up

Export Citation Format

Share Document