Two-grid Methods for Finite Volume Element Approximations of Nonlinear Sobolev Equations. (3rd March 2016)

• Record Type: Journal Article
• Authors: Yan, Jinliang; Zhang, Qian; Zhu, Ling; Zhang, Zhiyue
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 3(2016)
• Page Start: 391
• Page End: 414
• Publication Date: 2016-03-03
• Subjects: Error estimates -- finite volume element method -- Sobolev equations -- two-grid methods; 65M60 -- 65M15 -- 35K55; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2015.1115415
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, two-grid methods are studied for solving nonlinear Sobolev equation using the finite volume element method. The methods are based on one coarse grid space and one fine grid space. The nonsymmetric and nonlinear iterations are only executed on the coarse grid (with grid size H ), and the fine grid solution (with grid size h ) can be obtained in a single symmetric and linear step. The optimal H 1 error estimates are presented for the proposed methods, which show that the two-grid methods achieve optimal approximation as long as the mesh sizes satisfy h = 𝒪( H 3 |ln H |). As a result, solving such a large class of nonlinear Sobolev equations will not be much more difficult than solving one linearized equation.