BannerHauptseite TUMHauptseite LehrstuhlMathematik SchriftzugHauptseite LehrstuhlHauptseite Fakultät

Mortar finite element methods

Originally introduced as a domain decomposition method for the coupling of spectral elements, these techniques are used in a large class of nonconforming situations. Thus, the coupling of different physical models, discretization schemes, or non-matching triangulations along interior interfaces of the domain can be analyzed by mortar methods. These domain decomposition techniques provide a more flexible approach than standard conforming formulations. They are of special interest for time dependent problems, rotating geometries, diffusion coefficients with jumps, problems with local anisotropies, corner singularities, and when different terms dominate in different regions of the simulation domain. One major requirement is that the interface between the different regions is handled appropriately. Very often suitable matching conditions at the interfaces are formulated as weak continuity conditions. The analysis of the resulting jump terms across the interfaces plays an essential role for the a priori estimates of the discretization schemes. In particular, optimal methods can only be obtained if the consistency error is small enough compared with the best approximation error on the different subdomain.

Introduction to mortar methods (PDF in German)