Logically Rectangular Mixed Methodsfor Groundwater Flow and Transporton

We consider an extended mixed nite element formulation for groundwater ow 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 deened 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 modiied tensor coeecient. Special quadrature rules are introduced to transform the mixed method into a simple cell-centered nite diierence 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 ow, linear Galerkin procedures give rst order accurate velocities, while our method is second order accurate. Both computational and theoretical results are given.