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A Quadratic Triangular Finite Volume Element Method for a Semilinear Elliptic Equation

Part of:Partial differential equations, boundary value problems

Published online by Cambridge University Press:  11 October 2016

Zhiguang Xiong and
Kang Deng
Zhiguang Xiong*
Affiliation:
School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China
Kang Deng*
Affiliation:
School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China
*
*Corresponding author. Email:zgxiong@hnust.edu.cn (Z. G. Xiong), kdeng@hnust.edu.cn (K. Deng)
*Corresponding author. Email:zgxiong@hnust.edu.cn (Z. G. Xiong), kdeng@hnust.edu.cn (K. Deng)

Abstract

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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.

Keywords

Semilinear elliptic equationtriangulationfinite volume element with interpolated coefficients

MSC classification

Secondary:65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 1 , February 2017, pp. 186 - 204
Copyright
Copyright © Global-Science Press 2017 

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