ABSTRACT:
Compatible discrete operator schemes aim at preserving basic properties of the continuous problem at the discrete level. We analyze a class of such schemes for a model elliptic problem. The cornerstone in the design of the scheme is the discrete Hodge operator linking discrete gradient and fluxes. We present the two abstract properties to be satisfied by this operator to achieve convergence. Then, we focus on the design of this operator using the concept of local gradient reconstruction. Finally, we present numerical examples.
ADDITIONAL INFORMATION:
http://cermics.enpc.fr/~ern/