An equilibrated a posteriori error estimator for an Interior Penalty Discontinuous Galerkin approximation of the p-Laplace problem-Reference-Cited by-同舟云学术

An equilibrated a posteriori error estimator for an Interior Penalty Discontinuous Galerkin approximation of the p-Laplace problem

Published:2021-12-01 Issue:6 Volume:36 Page:313-336
ISSN:0927-6467
Container-title:Russian Journal of Numerical Analysis and Mathematical Modelling
language:en
Short-container-title:

Author:

Hoppe Ronald H. W.¹²,Iliash Youri¹

Affiliation:

1. Department of Mathematics , University of Augsburg , Augsburg , Germany

2. Department of Mathematics , University of Houston , Houston , USA

Abstract

Abstract We are concerned with an Interior Penalty Discontinuous Galerkin (IPDG) approximation of the p-Laplace equation and an equilibrated a posteriori error estimator. The IPDG method can be derived from a discretization of the associated minimization problem involving appropriately defined reconstruction operators. The equilibrated a posteriori error estimator provides an upper bound for the discretization error in the broken W 1,p norm and relies on the construction of an equilibrated flux in terms of a numerical flux function associated with the mixed formulation of the IPDG approximation. The relationship with a residual-type a posteriori error estimator is established as well. Numerical results illustrate the performance of both estimators.

Publisher

Walter de Gruyter GmbH

Subject

Modeling and Simulation,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/rnam-2021-0026/pdf

Reference52 articles.

1. C. Amrouche and N. E. H. Seloula, Lp-theory for vector potentials and Sobolev’s inequalities for vector fields: Application to the Stokes equations with pressure boundary conditions. Math. Models Meth. Appl. Sci. 23 (2013), 37–92.

2. T. Ando, Contractive projections in Lp spaces. Pacific J. Math. 17 (1966), 391–405.

3. D. Arnold, F. Brezzi, B. Cockburn, and D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 (2002), 1749–1779.

4. J. W. Barrett and W. B. Liu, Finite element approximation of the p-Laplacian. Math. Comput. 61 (1993), 523–537.

5. L. Belenki, L. Diening, and C. Kreuzer, Optimality of an adaptive finite element method for the p-Laplacian equation. IMA J. Numer. Anal. 32 (2012), 484–510.