Convergence and quasi-optimality of an adaptive finite element method for semilinear elliptic problems on L2 errors. Issue 11 (1st November 2020) - Guo, Liming; Huang, Fenglin
Abstract : In this paper, we prove the convergence and quasi-optimality of an adaptive finite element method for semilinear elliptic problems on L 2 errors by keeping sufficiently mildly graded meshes. Additional refinements are made to keep the meshes sufficiently mildly graded, but we find that it does not compromise the quasi-optimality of the adaptive finite element method presented in this paper. Numerical examples are provided to illustrate our theoretical results.