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An Augmented DG Scheme for Porous Media Equations

In: Numerical Mathematics and Advanced Applications

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Listed:
  • T. P. Barrios

    (Universidad Católica de la Santísima Concepción, Departamento de Matemática y Física Aplicadas)

  • R. Bustinza

    (Universidad de Concepción, Departamento de Ingeniería Matemática)

Abstract

We present an augmented local discontinuous Galerkin scheme for Darcy flow, that is obtained adding suitable Galerkin least squares terms arising from constitutive and equilibrium equations. The well-posedness of the scheme is proved applying Lax Milgram’s theorem. Finally, we present an a posteriori error estimator, and include one numerical experiment showing that the estimator is reliable and efficient.

Suggested Citation

  • T. P. Barrios & R. Bustinza, 2008. "An Augmented DG Scheme for Porous Media Equations," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 315-322, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_37
    DOI: 10.1007/978-3-540-69777-0_37
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