EFFICIENT MIXED METHODS FOR GROUNDWATER FLOW
ON TRIANGULAR OR TETRAHEDRAL MESHES

TODD ARBOGAST, CLINT N. DAWSON, and PHILIP T. KEENAN

Abstract:
Simulating flow in porous media requires the solution
of elliptic or parabolic partial differential equations.  When the
computational domain is irregularly shaped, applying finite element
methods with triangular elements offers great flexibility.

The mixed finite element method has proven useful for solving flow
equations. The difficulty 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 finite difference method in the primary variable, thus
reducing the linear system to a sparse, symmetric, positive
(semi-)definite 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
finite differences in a manner suitable for use with triangular
elements.  Numerical examples illustrate the accuracy and efficiency
of these new methods.