Mortar finite elements with dual Lagrange multipliers: Some applications

Abstract

Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We consider mortar techniques with dual Lagrange multiplier spaces to couple different discretization schemes. It is well known that the discretization error for linear mortar finite elements in the energy norm is of order h. Here, we apply these techniques to curvilinear boundaries, nonlinear problems and the coupling of different model equations and discretizations.