An expanded mixed covolume element method for integro-differential equation of Sobolev type on triangular grids

Abstract

Abstract The expanded mixed covolume Element (EMCVE) method is studied for the two-dimensional integro-differential equation of Sobolev type. We use a piecewise constant function space and the lowest order Raviart-Thomas ( RT 0 $\mathit{RT}_{0}$ ) space as the trial function spaces of the scalar unknown u and its gradient σ and flux λ, respectively. The semi-discrete and backward Euler fully-discrete EMCVE schemes are constructed, and the optimal a priori error estimates are derived. Moreover, numerical results are given to verify the theoretical analysis.

Keywords

• integro-differential equation of Sobolev type
• expanded mixed covolume element method
• optimal a priori error estimate