A Quadratic Triangular Finite Volume Element Method for a Semilinear Elliptic Equation

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.