Two-grid finite element methods combined with Crank-Nicolson scheme for nonlinear Sobolev equations

• Published in: Advances in computational mathematics Vol. 45; no. 2; pp. 611 - 630
• Main Authors: Chen, Chuanjun, Li, Kang, Chen, Yanping, Huang, Yunqing
• Format: Journal Article
• Language: English
• Published: New York Springer US 02.04.2019; Springer Nature B.V
• Subjects: Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Crank-Nicholson method; Estimates; Finite element method; Mathematical analysis; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nonlinear equations; Nonlinear systems; Visualization; Workload; Nonlinear Sobolev equations; 65N15; Error estimates; Crank-Nicolson scheme; 65N08; Two-grid finite element method

In this paper, we present a second-order accurate Crank-Nicolson scheme for the two-grid finite element methods of the nonlinear Sobolev equations. This method involves solving a small nonlinear system on a coarse mesh with mesh size H and a linear system on a fine mesh with mesh size h , which can...