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

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

Year:    2017

Author:    Zhiguang Xiong, Kang Deng

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 1 : pp. 186–204

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2014.m63

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 1 : pp. 186–204

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Semilinear elliptic equation triangulation finite volume element with interpolated coefficients.

Author Details

Zhiguang Xiong

Kang Deng

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