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Volume 32, Issue 2
A Triangular Finite Volume Element Method for a Semilinear Elliptic Equation

Zhiguang Xiong & Yanping Chen

DOI: 10.4208/jcm.1310-FE3

J. Comp. Math., 32 (2014), pp. 152-168.

Published online: 2014-04

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  • Abstract

In this paper we extend the idea of interpolated coefficients for a semilinear problem to the triangular finite volume element method. We first introduce triangular finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation. We then 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 equation, Triangulation, Finite volume element with interpolated coefficients.

  • AMS Subject Headings

49J20, 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-32-152, author = {Zhiguang Xiong and Yanping Chen}, title = {A Triangular Finite Volume Element Method for a Semilinear Elliptic Equation}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {2}, pages = {152--168}, abstract = {

In this paper we extend the idea of interpolated coefficients for a semilinear problem to the triangular finite volume element method. We first introduce triangular finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation. We then 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1310-FE3}, url = {http://global-sci.org/intro/article_detail/jcm/9875.html} }
TY - JOUR T1 - A Triangular Finite Volume Element Method for a Semilinear Elliptic Equation AU - Zhiguang Xiong & Yanping Chen JO - Journal of Computational Mathematics VL - 2 SP - 152 EP - 168 PY - 2014 DA - 2014/04 SN - 32 DO - http://doi.org/10.4208/jcm.1310-FE3 UR - https://global-sci.org/intro/article_detail/jcm/9875.html KW - Semilinear elliptic equation, Triangulation, Finite volume element with interpolated coefficients. AB -

In this paper we extend the idea of interpolated coefficients for a semilinear problem to the triangular finite volume element method. We first introduce triangular finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation. We then 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.

Zhiguang Xiong and Yanping Chen. (2014). A Triangular Finite Volume Element Method for a Semilinear Elliptic Equation. Journal of Computational Mathematics. 32 (2). 152-168. doi:10.4208/jcm.1310-FE3
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