Abstract
We discuss the general mathematical conditions for solvability, stability and optimal error bounds of mixed finite element discretizations. Our objective is to present these conditions with relatively simple arguments. We present the conditions for solvability and stability by considering the general coefficient matrix of mixed finite element discretizations, and then deduce the conditions for optimal error bounds for the distance between the finite element solutions and the exact solution of the mathematical problem. To exemplify our presentation we consider the solutions of various example problems. Finally, we also present a numerical test that is useful to identify numerically whether, for the solution of the general Stokes flow problem, a given finite element discretization satisfies the stability and optimal error bound conditions.
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