A Cell-centered Finite Difference Method on Quadrilaterals

@inproceedings{Wheeler2006ACF,
title={A Cell-centered Finite Difference Method on Quadrilaterals},
author={Mary F. Wheeler and Ivan Yotov},
year={2006}
}

We develop a cell-centered finite difference method for elliptic problems on curvilinear quadrilateral grids. The method is based on the lowest order BrezziDouglas-Marini (BDM) mixed finite element method. A quadrature rule gives a blockdiagonal mass matrix and allows for local flux elimination. The method is motivated and closely related to the multipoint flux approximation (MPFA) method. An advantage of our method is that it has a variational formulation. As a result finite element techniques… CONTINUE READING