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AN ANALYSIS OF THREE DIFFERENT FORMULATIONS OF THE DISCONTINUOUS GALERKIN METHOD FOR DIFFUSION EQUATIONS

MENGPING ZHANG

Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China

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and

CHI-WANG SHU

Division of Applied Mathematics, Brown University, Providence, RI 02912, USA

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https://doi.org/10.1142/S0218202503002568Cited by:92 (Source: Crossref)

Abstract

In this paper we present an analysis of three different formulations of the discontinuous Galerkin method for diffusion equations. The first formulation yields an numerically inconsistent and weakly unstable scheme, while the other two formulations, the local discontinuous Galerkin approach and the Baumann–Oden approach, give stable and convergent results. When written as finite difference schemes, such a distinction among the three formulations cannot be easily analyzed by the usual truncation errors, because of the phenomena of supraconvergence and weak instability. We perform a Fourier type analysis and compare the results with numerical experiments. The results of the Fourier type analysis agree well with the numerical results.

Dedicated to Professor Jim Douglas, Jr. on the occasion of his 75th birthday.

Keywords:

AMSC: 65M60, 65M12

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