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

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