Efficient Mixed Methods for Groundwater Flowon

Simulating ow in porous media requires the solution of elliptic or parabolic partial diierential equations. When the computational domain is irregularly shaped, applying nite element methods with triangular elements ooers great exibility. The mixed nite element method has proven useful for solving ow equations. The diiculty with mixed methods in general is in solving the linear algebraic systems that arise. On rectangular elements, the mixed method with lowest-order approximating spaces can be reduced to a simple nite diierence method in the primary variable, thus reducing the linear system to a sparse, symmetric, positive (semi-)deenite matrix , for which many solution techniques are known. This type of reduction is not straightforward for triangular elements. In this paper we outline new mixed type methods which generalize nite diierences in a manner suitable for use with triangular elements. Numerical examples illustrate the accuracy and eeciency of these new methods.