关于对流-扩散问题的Guermond-Pasquetti质量集总修正技术应用的注记
A note on the application of the Guermond-Pasquetti mass lumping correction technique for convection-diffusion problems
摘要：
我们提供了Guermond-Pasquetti质量集总校正技术的仔细傅里叶分析[Guermond J.- L.，帕斯奎提河输运问题质量集总色散效应的修正技术。- 应用力学与工程计算机方法。- 2013. - 第253卷- P. 186-198]应用于纯输运和对流-扩散问题。特别是，它被发现，增加校正的数量减少了扩散问题的准确性，然而，所有的校正方案是更准确的比一致的Galerkin制定在这种情况下。对于纯运输问题，情况正好相反。我们还研究了两个数值解-一致解和修正解之间的差异，并表明，增加修正的数量使得修正方案的解在所有情况下都更接近一致解。
英文摘要：
We provide a careful Fourier analysis of the Guermond-Pasquetti mass lumping correction technique [Guermond J.-L., Pasquetti R. A correction technique for the dispersive effects of mass lumping for transport problems. - Computer Methods in Applied Mechanics and Engineering. - 2013. - Vol. 253. - P. 186-198] applied to pure transport and convection-diffusion problems. In particular, it is found that increasing the number of corrections reduces the accuracy for problems with diffusion; however all the corrected schemes are more accurate than the consistent Galerkin formulation in this case. For the pure transport problems the situation is the opposite. We also investigate the differences between two numerical solutions - the consistent solution and the corrected ones, and show that increasing the number of corrections makes solutions of the corrected schemes closer to the consistent solution in all cases.
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