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Non-conforming domain decomposition methods

Domain decomposition methods are powerful tools to solve the partial differential equations arising from many engineering applications. The domain is decomposed into several non-overlapping subdomains, and the problem is assembled from smaller subproblems corresponding to these subdomains.
Non-conforming methods are of interest if the meshes of neighboring subdomains do not fit together, or if adaptive remeshing is used in some subdomains. Thus, non-conforming methods yield a more flexible approach for the discretization than conforming methods. They also yield a flexible tool for the coupling of different discretization schemes and for different physical models in the subdomains. We are interested in the analysis and numerics of mortar and Nitsche techniques, which allow weak coupling of the subdomains. Efficient multigrid methods can be used in the framework of mortar techniques with dual Lagrange multipliers. We can also use efficient multigrid methods in Nitsche techniques. For the Nitsche case, no Lagrange multiplier is necessary. However a stability parameter is required.

Introduction to non-conforming domain decomposition methods (PDF in German)