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Error Estimates for an LDG Method Applied to Signorini Type Problems

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Abstract

In this paper we propose and analyze a Local Discontinuous Galerkin method for an elliptic variational inequality of the first kind that corresponds to a Poisson equation with Signorini type condition on part of the boundary. The method uses piecewise polynomials of degree one for the field variable and of degree zero or one for the approximation of its gradient. We show optimal convergence for the method and illustrate it with some numerical experiments.

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Authors and Affiliations

  1. CI²MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Rommel Bustinza

  2. Dep. Matemática Aplicada, CPS, Universidad de Zaragoza, 50018, Zaragoza, Spain

    Francisco-Javier Sayas

  3. Dept. Mathematical Sciences, University of Delaware, 501 Ewing Hall, Newark, DE, 19716, USA

    Francisco-Javier Sayas

Authors
  1. Rommel Bustinza
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  2. Francisco-Javier Sayas
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Correspondence to Rommel Bustinza.

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Bustinza, R., Sayas, FJ. Error Estimates for an LDG Method Applied to Signorini Type Problems. J Sci Comput 52, 322–339 (2012). https://doi.org/10.1007/s10915-011-9548-5

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  • DOI: https://doi.org/10.1007/s10915-011-9548-5

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