Uniqueness of discrete solutions of nonmonotone PDEs without a globally fine mesh condition
arXiv:1704.043197 citations
AI Analysis
Provides a theoretical guarantee for uniqueness in numerical solutions of nonmonotone PDEs, addressing a known gap in finite element analysis.
The paper proves uniqueness of finite element solutions for nonmonotone elliptic PDEs in 1D and 2D using a local variation bound, without requiring a globally small meshsize.
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.