Mixed finite element methods for elliptic obstacle problems

TL;DR

This paper introduces mixed finite element methods for elliptic obstacle problems, incorporating obstacle forces as unknowns, and provides error estimates supported by numerical experiments.

Contribution

It proposes novel mixed formulations for obstacle problems, including force as an unknown, and derives new error estimates with numerical validation.

Findings

Effective a priori and a posteriori error estimates

Numerical experiments confirm theoretical results

Inclusion of obstacle force as an unknown improves modeling accuracy

Abstract

Mixed variational formulations for the first-order system of the elastic membrane obstacle problem and the second-order system of the Kirchhoff--Love plate obstacle problem are proposed. The force exerted by the rigid obstacle is included as a new unknown. A priori and a posteriori error estimates are derived for both obstacle problems. The a posteriori error estimates are based on conforming postprocessed solutions. Numerical experiments conclude this work.