A note on least-squares mixed finite elements in relation to standard and mixed finite elements

摘要

The least-squares mixed finite-element method for second-order elliptic problems yields an approximation u(h) is an element of V-h subset of H-0(1)(Omega) of the potential u together with an approximation p(h) is an element of Gamma(h) subset of H(div ; Omega) of the vector field p = -A del u. Comparing u(h) with the standard finite-element approximation of u in V-h, and p(h) with the mixed finite-element approximation of p, it turns out that they are higher-order perturbations of each other. In other words, they are 'superclose'. Refined a priori bounds and superconvergence results can now be proved. Also, the local mass conservation error is of higher order than could be concluded from the standard a priori analysis.