Abstract. We consider the parallel solution of elliptic boundary value problems discretized by domain decomposition methods on nonmatching grids involving mortar finite elements. We start from an initial nonoverlapping decomposition of the computational domain and independent triangulations of the subdomains realizing weak continuity conditions on the internal subdomain boundaries by means of appropriately chosen Lagrangian multipliers. The solution process features a preconditioned Lanczos iteration for the resulting saddle point problem using a block diagonal preconditioner and an adaptive local mesh refinement on the basis of efficient and reliable residual based or hierarchical a posteriori error estimators. In the parallel implementation of the code, the data related to the subdomains are appropriately distributed among the available processors. The efficiency of the parallel implementation and the benefits of the adaptive grid refinement process are illustrated by numerical simulation results obtained on a IBM SP2 for some selected test problems including fully potential flow around profiles. Key words: domain decomposition on nonmatching grids, mortar finite element methods, substructuring preconditioners, adaptive grid refinement, a posteriori error estimators AMS (MOS) Subject Classification: 65N15,65N30,65N50,65N55 1.
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