Abstract
In this paper we systematically reviewthe control volume finite element (CVFE) methods for numericalsolutions of second-order partial differential equations.Their relationships to the finite differenceand standard (Galerkin) finite element methods are considered.Through their relationshipto the finite differences, upstream weightedCVFE methods and the conditions on positivetransmissibilities (positive flux linkages)are studied. Through their relationshipto the standard finite elements,error estimates forthe CVFE are obtained. These estimates arecomparable to those for the standard finite element methodsusing piecewise linear elements. Finally, anapplication to multiphase flows in porousmedia is presented.
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