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 solution over each element. The uniqueness follows from this result, and does not require a globally small meshsize.
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The authors would like to acknowledge an anonymous reviewer for feedback which helped to clarify several issues in this manuscript.
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SP was supported in part by NSF DMS 1719849. YZ was supported in part by NSF DMS-1319110.
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Pollock, S., Zhu, Y. Uniqueness of discrete solutions of nonmonotone PDEs without a globally fine mesh condition. Numer. Math. 139, 845–865 (2018). https://doi.org/10.1007/s00211-018-0956-4
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DOI: https://doi.org/10.1007/s00211-018-0956-4