Two-grid finite element method and its a posteriori error estimates for a nonmonotone quasilinear elliptic problem under minimal regularity of data. (1st July 2018)

• Record Type: Journal Article
• Authors: Bi, Chunjia; Wang, Cheng; Lin, Yanping
• Is Part Of: Computers & mathematics with applications. Volume 76:issue 1(2018)
• Page Start: 98
• Page End: 112
• Publication Date: 2018-07-01
• Subjects: Two-grid finite element method -- A posteriori error estimates -- Quasilinear elliptic problems; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.04.006
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we propose and analyze a two-grid finite element method for a class of quasilinear elliptic problems under minimal regularity of data in a bounded convex polygonal Ω ⊂ R 2, which can be thought of as a type of linearization of the nonlinear system using a solution from a coarse finite element space. With this technique, solving a quasilinear elliptic problem on the fine finite element space is reduced into solving a linear problem on the fine finite element space and solving the quasilinear elliptic problem on a coarse space. Convergence estimates in the H 1 -norm are derived to justify the efficiency of the proposed two-grid algorithm. Moreover, we propose a natural and computationally efficient residual-based a posteriori error estimator of the two-grid finite element method for this nonmonotone quasilinear elliptic problem and derive the global upper and lower bounds on the error in the H 1 -norm. Numerical experiments are provided to confirm our theoretical findings.