Finite volume element method with interpolated coefficients for two-point boundary value problem of semilinear differential equations

In this paper we extend the idea of interpolated coefficients for semilinear problems to the finite volume element methods. At first we introduce linear finite volume element method with interpolated coefficients for two-point boundary value problem of semilinear differential equations. Next we derive convergence estimate in H1 norm and superconvergence of derivative. Finally an example is given to illustrate the effectiveness of the proposed method.