A unified physical presentation of mixed, mixed-hybrid finite elements and standard finite difference approximations for the determination of velocities in waterflow problems

Abstract

The need for more precise simulation of the transport of pollutants by underground water has drawn the attention of hydrologists to a class of approximation techniques known by the generic name of Mixed Finite Element Methods. The basic idea here is to approximate simultaneously the pressure P and its gradient, or more generally a gradient related velocity field q in such a way that both P h and q h can be proved to converge, in adequate norms, to their continuous counterparts, and that the approximated velocity field q h retains one important feature of the exact velocity field q, namely that it is continuous on each element and has a continuous normal component when passing from one element to the other