Adaptive finite element method for nonmonotone quasi-linear elliptic problems. (1st July 2021)

• Record Type: Journal Article
• Authors: Guo, Liming; Bi, Chunjia
• Is Part Of: Computers & mathematics with applications. Volume 93(2021)
• Page Start: 94
• Page End: 105
• Publication Date: 2021-07-01
• Subjects: Adaptive finite element method -- Convergence -- Quasi-optimality -- Nonmonotone -- Quasi-linear elliptic problems; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.03.034
• Languages: English
• ISSNs: 0898-1221

Abstract

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.