Discontinuous Mixed Covolume Methods for Linear Parabolic Integrodifferential Problems

Abstract

The semidiscrete and fully discrete discontinuous mixed covolume schemes for the linear parabolic integrodifferential problems on triangular meshes are proposed. The error analysis of the semidiscrete and fully discrete discontinuous mixed covolume scheme is presented and the optimal order error estimate in discontinuous $H(\mathrm{\text{d}}\mathrm{\text{i}}\mathrm{\text{v}})$ and first-order error estimate in $L^2$ are obtained with the lowest order Raviart-Thomas mixed element space.