Convergence and quasi-optimality of an adaptive finite element method for semilinear elliptic problems on L2 errors. Issue 11 (1st November 2020)

• Record Type: Journal Article
• Authors: Guo, Liming; Huang, Fenglin
• Is Part Of: International journal of computer mathematics. Volume 97:Issue 11(2020)
• Page Start: 2337
• Page End: 2354
• Publication Date: 2020-11-01
• Subjects: Adaptive finite element method -- convergence -- quasi-optimality -- semilinear elliptic problems -- L2 errors; 65N30 -- 65N15; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2019.1698734
• Languages: English
• ISSNs: 0020-7160

Abstract

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.