LOGICALLY RECTANGULAR MIXED METHODS
FOR GROUNDWATER FLOW AND TRANSPORT
ON GENERAL GEOMETRY

TODD ARBOGAST, MARY F. WHEELER, and IVAN YOTOV

Abstract:
We consider an extended mixed finite element formulation for
groundwater flow and transport problems with either a tensor hydraulic
conductivity or a tensor dispersion.  While the aquifer domain can be
geometrically general, in our formulation the computational domain is
rectangular.  The approximating spaces for the mixed method are
defined on a smooth curvilinear grid, obtained by a global mapping of
the rectangular, computational grid.  The original problem is mapped
to the computational domain, giving a similar problem with a modified
tensor coefficient.  Special quadrature rules are introduced to
transform the mixed method into a simple cell-centered finite
difference method with a 9 point stencil in 2-D and 19 point stencil
in 3-D.  The resulting scheme is locally mass conservative.  In the
case of flow, linear Galerkin procedures give first order accurate
velocities, while our method is second order accurate.  Both
computational and theoretical results are given.