Adaptive finite element method for nonmonotone quasi-linear elliptic problems. (1st July 2021) - Guo, Liming; Bi, Chunjia
Abstract: In this paper, we study the simplest and the most standard adaptive finite element method for the second-order nonmonotone quasi-linear elliptic problems with the exact solution u ∈ H 0 1 + α ( Ω ), α ≥ 1 2 . The adaptive algorithm is based on the residual-based a posteriori error estimators and Dörfler's marking strategy. We prove the convergence and quasi-optimality of the adaptive finite element method when the initial mesh is sufficiently fine. Numerical experiments are provided to illustrate our findings.