First-Order Least-Squares Method for the Obstacle Problem
Numerical Analysis
2018-01-30 v1
Abstract
We define and analyse a least-squares finite element method for a first-order reformulation of the obstacle problem. Moreover, we derive variational inequalities that are based on similar but non-symmetric bilinear forms. A priori error estimates including the case of non-conforming convex sets are given and optimal convergence rates are shown for the lowest-order case. We provide also a posteriori bounds that can be be used as error indicators in an adaptive algorithm. Numerical studies are presented.
Cite
@article{arxiv.1801.09622,
title = {First-Order Least-Squares Method for the Obstacle Problem},
author = {Thomas Führer},
journal= {arXiv preprint arXiv:1801.09622},
year = {2018}
}