Finite Element Methods on Non-conforming Grids by Penalizing the Matching Constraint

The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence. Mathematics Subject Classification. 65N12, 65N30, 65F10. Received: June 25, 2002. Revised: December 17, 2002.