Error analysis of Nitsche's mortar method

TL;DR

This paper derives optimal error estimates for Nitsche's mortar finite element method, demonstrating its robustness in handling large material and mesh parameter jumps through theoretical analysis and numerical validation.

Contribution

It provides the first comprehensive a priori and a posteriori error analysis for Nitsche's mortar method, establishing its robustness and equivalence to stabilized mixed methods.

Findings

Error estimates are optimal and robust.

Numerical results confirm estimator robustness.

Method handles large parameter jumps effectively.

Abstract

Optimal a priori and a posteriori error estimates are derived for Nitsche's mortar finite elements. The analysis is based on the equivalence of the Nitsche's method and the stabilised mixed method. The Nitsche's method is defined so that it is robust with respect to large jumps in the material and mesh parameters over the interface. Numerical results demonstrate the robustness of the a posteriori estimators.