Volume 9, Issue 1
A Quadratic Triangular Finite Volume Element Method for a Semilinear Elliptic Equation

Adv. Appl. Math. Mech., 9 (2017), pp. 186-204.

Published online: 2018-05

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• 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.

• Keywords

Semilinear elliptic equation, triangulation, finite volume element with interpolated coefficients.

65N30

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@Article{AAMM-9-186, author = {}, title = {A Quadratic Triangular Finite Volume Element Method for a Semilinear Elliptic Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m63}, url = {http://global-sci.org/intro/article_detail/aamm/12144.html} }
TY - JOUR T1 - A Quadratic Triangular Finite Volume Element Method for a Semilinear Elliptic Equation JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 186 EP - 204 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2014.m63 UR - https://global-sci.org/intro/article_detail/aamm/12144.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 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.

Zhiguang Xiong & Kang Deng. (2020). A Quadratic Triangular Finite Volume Element Method for a Semilinear Elliptic Equation. Advances in Applied Mathematics and Mechanics. 9 (1). 186-204. doi:10.4208/aamm.2014.m63
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