Uniqueness of discrete solutions of nonmonotone PDEs without a globally fine mesh condition

Abstract

Uniqueness of the finite element solution for nonmonotone quasilinear problems of elliptic type is established in one and two dimensions. In each case, we prove a comparison theorem based on locally bounding the variation of the discrete so- lution over each element. The uniqueness follows from this result, and does not require a globally small meshsize.