A toolbox for a class of discontinuous Petrov-Galerkin methods using trilinos.

Abstract

The class of discontinuous Petrov-Galerkin finite element methods (DPG) proposed by L. Demkowicz and J. Gopalakrishnan [4,5] guarantees the optimality of the solution in an energy norm and produces a symmetric positive definite stiffness matrix, among other desirable properties. In this paper, we describe a toolbox, implemented atop Sandia's Trilinos library, for rapid development of solvers for DPG methods. We use this toolbox to develop solvers for the Poisson and Stokes problems.4