A Local Post-Processing Technique for Improving the Accuracy in Mixed Finite-Element Approximations

A general simple post-processing technique is given in this paper. Under certain conditions, if an algorithm approximating a function u also provides a good approximation for its gradient and for some locally defined projection $Pu$, then by this method, a better approximation for u can be easily obtained. Essentially, the leading term of the error between u and its original approximation can be computed. It is shown how the method may be applied to various mixed type finite-element methods.