A Triangular Finite Volume Element Method for a Semilinear Elliptic Equation (Journal of Computational Mathematics, 2018)
In this paper we extend the idea of interpolated coefficients for a semilinear problem to the triangular finite volume element method. We first introduce triangular finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation. We then 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.