Rommel Bustinza, Francisco J. Sayas:
Error estimates for an LDG method applied to Signorini type problems
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.
This preprint gave rise to the following definitive publication(s):
Rommel BUSTINZA, Francisco J. SAYAS: Error estimates for an LDG method applied to Signorini type problems. Journal of Scientific Computing, vol. 52, 2, pp. 322-339, (2012).