A Quadratic Triangular Finite Volume Element Method for a Semilinear Elliptic Equation. Issue 1 (11th October 2016)

• Record Type: Journal Article
• Authors: Xiong, Zhiguang; Deng, Kang
• Is Part Of: Advances in applied mathematics and mechanics. Volume 9:Issue 1(2017)
• Page Start: 186
• Page End: 204
• Publication Date: 2016-10-11
• Subjects: 65N30; Semilinear elliptic equation, -- triangulation, -- finite volume element with interpolated coefficients; Engineering mathematics -- Periodicals; Mechanics -- Periodicals; 620.00151825
• DOI: 10.4208/aamm.2014.m63
• Languages: English
• ISSNs: 2070-0733

Abstract

Abstract: In this paper we extend the idea of interpolated coefficients for a semilinear problem to the quadratic triangular finite volume element method. At first we introduce quadratic triangular finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation. Next we derive convergence estimate in H 1 -norm, L 2 -norm and L ∞ -norm, respectively. Finally an example is given to illustrate the effectiveness of the proposed method.