University of Colorado at Denver and Health Sciences Center A Petrov-Galerkin Enriched Method: A Mass Conservative Finite Element Method For The Darcy Equation

We present novel enhanced finite element methods for the Darcy problem starting from the non stable continuous P1/P0 finite element space enriched with multiscale functions. The methods are derived in a Petrov-Galerkin framework where both velocity and pressure trial spaces are enriched with functions based on residuals of the strong equations in each element and edge partition. The strategy leads to a velocity space enhanced with functions of the lowest order Raviart-Thomas space and to a stable weak formulation preserving the local mass conservation feature. Several numerical tests validate the methods.