Galerkin least squares finite element method for the obstacle problem
Numerical Analysis
2016-11-23 v1
Abstract
We construct a consistent multiplier free method for the finite element solution of the obstacle problem. The method is based on an augmented Lagrangian formulation in which we eliminate the multiplier by use of its definition in a discrete setting. We prove existence and uniqueness of discrete solutions and optimal order a priori error estimates for smooth exact solutions. Using a saturation assumption we also prove an a posteriori error estimate. Numerical examples show the performance of the method and of an adaptive algorithm for the control of the discretization error.
Cite
@article{arxiv.1609.03431,
title = {Galerkin least squares finite element method for the obstacle problem},
author = {Erik Burman and Peter Hansbo and Mats G. Larson and Rolf Stenberg},
journal= {arXiv preprint arXiv:1609.03431},
year = {2016}
}
Comments
18 pages, 5 figures