Higher order mortar finite elements with dual Lagrange multiplier spaces and applications (original) (raw)

The numerical approximation of partial differential equations coming from physical and engineering modeling is often a challenging task. Most often these partial differential equations are discretized with finite elements and can be solved by modern super-computers. Working with different discretization techniques in different subdomains or independent triangulations, the challenging task is to couple these different discretization schemes or non-matching triangulation without losing the optimality of the approach. Mortar methods yield optimal and flexible coupling techniques for different discretization schemes. Especially when combined with dual Lagrange multiplier spaces, the efficient realization of the weak matching condition is possible, and efficient multigrid methods can be adapted to the non-conforming situation. In this thesis, we concentrate on higher order dual Lagrange multiplier spaces for mortar finite elements. These non-standard Lagrange multipliers show the same qu...