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

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.

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