Domain decomposition for multi-dimensional, first order systems of partial differential equations

Abstract

We consider a general, variationally based, domain decomposition method for positive symmetric systems. This procedure contains as a special case the frequently used method of assigning matching conditions across interfaces based upon inflow and outflow characteristics. The correct method of monitoring the possible convergence of various methods is studied as well as the error in a finite element discretization of the resulting split-up subproblems.

Keywords:

• Domain decomposition
• Friedrichs'systems
• positive symmetric system
• substructuring

AMS:

• 65N30
• 65N15