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

Zhiguang Xiong & Kang Deng

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 H1 -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

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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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 H1 -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} }
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