A Postprocessed Flux Conserving Finite Element Solution.

We propose a local postprocessing method to get a new finite element solution whose flux is conservative element-wise. First, we use the so-called polynomial preserving recovery (postprocessing) technique to obtain a higher order flux which is continuous across the element boundary. Then, we use special bubble functions, which have a nonzero flux only on one face-edge or face-triangle of each element, to correct the finite element solution element by element, guided by the above super-convergent flux and the element mass. The new finite element solution preserves mass element-wise and retains the quasioptimality in approximation. The method produces a conservative flux, of high-order accuracy, satisfying the constitutive law. Numerical tests in 2D and 3D are presented. [ABSTRACT FROM AUTHOR]