Analysis and Parallel Implementation of Adaptive Mortar Element Methods

Abstract

We consider the development, analysis, and parallel implementation of domain decomposition techniques on nonmatching grids, also known as the mortar element approach, for the numerical solution of elliptic boundary value problems. The methods are based on a macro-hybrid variational formulation with respect to a nonoverlapping decomposition of the computational domain. They feature multilevel block preconditioned Lanczos type algorithms for the efficient iterative solution and efficient and reliable hierarchical type a posteriori error estimators for adaptive local grid refinement. Aspects of parallelization such as load balancing are also addressed in some detail. Numerical results are given to illustrate the asymptotically optimal computational complexity and parallel efficiency of the solvers as well as the effectivity of the a posteriori error estimators.