Collection of abstracts 13th GAMM-Seminar Kiel on Numerical Treatment of Multi-Scale Problems January 24th to 26th, 1997.

Sunday, January 26th, 1997

A note on an adaptive nonoverlapping domain decomposition method for elliptic problems

We consider a nonoverlapping domain decomposition method for elliptic boundary value problems with adaptive interface conditions. The method can be derived from the fictitious overlapping technique (by P.L. Lions). The design of the interface conditions generalizes an idea of Rogier / Nataf for advection dominated problems.

The method is applicable to the following classes: scalar linear elliptic boundary value problems of second order, linear elasticity problem, linearized Navier-Stokes or Oseen equations (including Stokes).

We prove strong H^1-convergence of the method for the continuous case. Furthermore we present numerical results using a stabilized Galerkin finite element method. The numerical convergence rate is shown to be very reasonable even in case of highly advection or reaction dominated situations.