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 - <p style="text-align: justify;">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.</p>