TY - JOUR T1 - A New Discontinuous Galerkin Method for Parabolic Equations with Discontinuous Coefficient JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 325 EP - 342 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.y11038 UR - https://global-sci.org/intro/article_detail/nmtma/5906.html KW - Parabolic equation, discontinuous coefficient, discontinuous Galerkin method, error estimate, stability analysis. AB -

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.