CRPC-TR97685							January 1997

Title: Logically Rectangular Mixed Methods for Flow in Irregular, 
Heterogeneous Domains

Authors: T. Arbogast, M.F. Wheeler, I. Yotov

Abstract:
We develop and analyze a mixed finite element and a cell-centered finite 
difference method for groundwater flow in an irregular, heterogeneous, 
multi-block aquifer domain. The methods are designed to handle full 
tensor hydraulic conductivity with possible discontinuities. The domain 
can be divided into a series of smaller, non-overlapping sub-domain 
blocks of irregular geometry. Each is covered by a logically rectangular 
grid; these are not required to match on the interface so that we can 
model faults, local refinements, and other internal boundaries, such as 
interfaces where the conductivity is disconinuous. After continuously 
mapping each sub-domain to a rectangular reference sub-domain, all 
computations can be performed in a simple rectangular context. Standard 
mixed finite element spaces are used for the local sub-domain 
discretization. A "mortar" finite element space is introduced to 
accurately approximate the pressure along the sub-domain interfaces. 
Quadrature rules are employed to transform the mixed finite element 
method into cell-centered finite differences for the pressures. 
Theoretical and computational results show that the scheme is highly 
accurate. Superconvergence for both pressure and velocity is obtained at 
certain discrete points. Three dimensional numerical examples using an 
efficient parallel domain decomposition solver are also presented.