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An a posteriori error analysis of an augmented discontinuous Galerkin formulation for Darcy flow

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Abstract

In this paper we develop an a posteriori error analysis for an augmented discontinuous Garlerkin formulation applied to the Darcy flow. More precisely, we derive a reliable and efficient a posteriori error estimator, which consists of residual terms. Finally, we present several numerical experiments, showing the robustness of the method and the theoretical properties of the estimator, thus confirming the capability of the corresponding adaptive algorithms to localize the inner layers, the singularities and/or the large stress regions of the exact solution.

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Authors and Affiliations

  1. Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Casilla 297, Concepción, Chile

    Tomás P. Barrios

  2. CI2MA and Departamento de Ingenierí a Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Rommel Bustinza

Authors
  1. Tomás P. Barrios
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  2. Rommel Bustinza
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Correspondence to Rommel Bustinza.

Additional information

This research was partially supported by Centro de Investigación en Ingeniería Matemática (CI2MA), Universidad de Concepción, by CONICYT-Chile through the FONDECYT Grants No. 1080168 and No. 11060014, by the Dirección de Investigación of the Universidad Católica de la Santísima Concepción, and by BASAL project CMM, Universidad de Chile.

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Barrios, T.P., Bustinza, R. An a posteriori error analysis of an augmented discontinuous Galerkin formulation for Darcy flow. Numer. Math. 120, 231–269 (2012). https://doi.org/10.1007/s00211-011-0410-3

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  • DOI: https://doi.org/10.1007/s00211-011-0410-3

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