Mixed finite volume method for nonlinear elliptic problems

Abstract

In this article we construct and analyze a mixed finite volume method for second-order nonlinear elliptic problems employing H(div; Omega)-conforming approximations for the vector variable and completely discontinuous approximations for the scalar variable. The main attractive feature of our method is that, although the vector variable is H(div; Omega)-conforming, one can eliminate it in a local manner to obtain a discontinuous Galerkin method for the scalar variable. Optimal error estimates will be established for both vector and scalar variables. We also present a fully discrete version of this method that is more convenient for computational purposes. (c) 2005 Wiley Periodicals, Inc.