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Volume 6, Issue 2
A New Discontinuous Galerkin Method for Parabolic Equations with Discontinuous Coefficient

Rongpei Zhang, Xijun Yu, Xia Cui, Xiaohan Long & Tao Feng

DOI: 10.4208/nmtma.2013.y11038

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 325-342.

Published online: 2013-06

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  • 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.

  • Keywords

Parabolic equation, discontinuous coefficient, discontinuous Galerkin method, error estimate, stability analysis.

  • AMS Subject Headings

65M60, 35K05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-6-325, author = {Rongpei Zhang, Xijun Yu, Xia Cui, Xiaohan Long and Tao Feng}, title = {A New Discontinuous Galerkin Method for Parabolic Equations with Discontinuous Coefficient}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {2}, pages = {325--342}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.y11038}, url = {http://global-sci.org/intro/article_detail/nmtma/5906.html} }
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 -

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.

Rongpei Zhang, Xijun Yu, Xia Cui, Xiaohan Long and Tao Feng. (2013). A New Discontinuous Galerkin Method for Parabolic Equations with Discontinuous Coefficient. Numerical Mathematics: Theory, Methods and Applications. 6 (2). 325-342. doi:10.4208/nmtma.2013.y11038
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