TY - JOUR T1 - A Quadratic Triangular Finite Volume Element Method for a Semilinear Elliptic Equation AU - Xiong , Zhiguang AU - Deng , Kang 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.