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A New Discontinuous Galerkin Method for Parabolic Equations with Discontinuous Coefficient

A New Discontinuous Galerkin Method for Parabolic Equations with Discontinuous Coefficient

Year:    2013

Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 2 : pp. 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 L2 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 O(hk). Numerical examples for both 1-dimensional and 2-dimensional problems demonstrate the validity of the new method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2013.y11038

Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 2 : pp. 325–342

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Parabolic equation discontinuous coefficient discontinuous Galerkin method error estimate stability analysis.

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