A unified physical presentation of mixed, mixed-hybrid finite elements and usual finite differences for the determination of velocities in waterflow problems

The objective of this paper is to give a non-mathematical presentation of mixed finite elements, following as much as possible physical intuition and natural good sense. Mixed and mixed hybrid finite elements are clearly presented as two formulations of the same approximation and the use of a quadrature rule is shown to reduce both formulations to the usual finite difference scheme. Application to the resolution of stationary (elliptic) and time dependent (parabolic) water flow problems is discussed in detail for the case of a uniform rectangular grid, and the enhancement in the approximation of velocities is emphasized. Generalizations and order of convergence are discussed