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Enhancement of the accuracy of the Green element method:Application to potential problems

机译：增强绿色元素方法的准确性：应用于潜在问题

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摘要

The 2-D formulation of the Green element method (GEM) which approximates the internal normal directional fluxes by difference expressions in terms of the field variable had been recognized to be fraught with errors that comprise its accuracy. However, this approach is computational attractive because there is only one degree of freedom at every node, the system matrix is slender, and it does require additional compatibility relationships. There have been attempts to reduce the numerical errors of this original GEM formulation by the use of flux-based formulations which essentially retain the internal fluxes but at the expense of those attractive numerical features. Here the original GEM is revisited and shown that, with difference approximation of the internal normal fluxes whose error is of the order of the square of the size of the element, its accuracy is greatly enhanced to a level comparable to the flux-based formulations. This approach is demonstrated on regular domains with rectangular elements and irregular domains with triangular elements using six examples that cover steady, transient, linear and nonlinear potential flow and heat transfer problems in homogeneous and heterogeneous media.
机译：格林元件法（GEM）的二维公式通过场场变量的差异表达式近似内部法向通量，已被认为充满了误差，其中包括其精度。但是，此方法在计算上很有吸引力，因为每个节点只有一个自由度，系统矩阵很细长，并且确实需要其他兼容性关系。已经尝试通过使用基于通量的配方来减少该原始GEM配方的数值误差，该基于通量的配方基本上保留了内部通量，但是以那些吸引人的数值特征为代价。在这里，原始的GEM被重新研究并显示出，通过内部法线通量的差异近似，其误差为元件尺寸的平方的数量级，其精度大大提高到了与基于通量的配方相当的水平。使用六个示例说明了在矩形元素的规则区域和三角形元素的不规则区域上使用的六个方法，这些方法涵盖了均质和非均质介质中的稳态，瞬态，线性和非线性势能流动和传热问题。

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