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

  • Ronald H. W. Hoppe EMAIL logo und Youri Iliash
Veröffentlicht/Copyright: 3. Dezember 2021

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 W1,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.

MSC 2010: 65N30; 65N15; 65N50
  1. funding The work has been supported by the NSF grant DMS-1520886.

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Received: 2021-06-02
Accepted: 2021-09-28
Published Online: 2021-12-03
Published in Print: 2021-12-20

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 3.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/rnam-2021-0026/html
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