TY - JOUR
T1 - A New Discontinuous Galerkin Method for Parabolic Equations with Discontinuous Coefficient
AU - Rongpei Zhang, Xijun Yu, Xia Cui, Xiaohan Long & Tao Feng
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 - <p style="text-align: justify;">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&nbsp;$\mathcal{O}(h^k)$. Numerical examples for both 1-dimensional and
2-dimensional problems demonstrate the validity of the new method.</p>