A New Discontinuous Galerkin Method for Parabolic Equations with Discontinuous Coefficient

Abstract

In this paper, a new discontinuous Galerkin method is developed for the parabolic equation with jump coefficients satisfying the continuous flow condition. Theoretical analysis shows that this method is $L^2$ stable. When the finite element space consists of interpolative polynomials of degrees $k$, the convergent rate of the semi-discrete discontinuous Galerkin scheme has an order of $\mathcal{O}(h^k)$. Numerical examples for both 1-dimensional and 2-dimensional problems demonstrate the validity of the new method.