二次元移流拡散方程式の有限要素法および差分法による新しい陽的定式化 : 誤差解析手法によるアプローチ

概要

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In our previous papers, the Modified Galerkin Method (MGM) was proposed for the one-dimensional and the two-dimensional convection-diffusion equations as one of the most efficient methods using the error analysis technique. In this paper, this approach was applied for two explicit finite element methods and eight explicit finite difference methods. The corresponding correction coefficients were obtained for these methods in order to improve their numerical accuracies. All of these newly formulated schemes were evaluated from the standpoints of phase error and dissipation error. From the error analysis results, we confirmed the higher accuracy of our proposed finite difference method for a convection dominated problem and our proposed finite element method for a diffusion dominated problem. Through numerical experiments using the explicit finite element schemes, we confirmed the effectiveness of our proposed method and the general correspondence between the error analysis and the numerical simulation.
社団法人日本機械学会の論文
1993-03-25