The streamline–diffusion method for nonconforming Qrot1 elements on rectangular tensor–product meshes
The streamline–diffusion method for nonconforming Qrot1 elements on rectangular tensor–product meshes
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DOI：
10.1093/imanum/21.1.123
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发表时间：
2001
影响因子：
2.1
通讯作者：
M. Stynes;L. Tobiska
中科院分区：
文献类型：
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作者：
M. Stynes;L. Tobiska
当流线扩散有限元法应用于对流扩散问题，使用试探空间，它以前已经观察到，稳定性和收敛问题可能会发生。因此，有人建议，某些跳跃项应添加到双线性形式，以获得相同的稳定性和收敛行为，在协调的情况下。本文的分析表明，对于矩形正则张量积网格上的Q1 rot元，不需要跳跃项来稳定方法。此外，在这种情况下，对于光滑的解决方案，我们得出的流线扩散范数收敛的顺序h 3/2（均匀的扩散系数的问题），其中h是网格直径。(This已知的情况下，估计是一致的。）我们的分析还表明，类似的稳定性和收敛性的结果不成立类似的分段线性插值元。
When the streamline-diffusion finite element method is applied to convection-diffusion problems using nonconforming trial spaces, it has previously been observed that stability and convergence problems may occur. It has consequently been proposed that certain jump terms should be added to the bilinear form to obtain the same stability and convergence behaviour as in the conforming case. The analysis in this paper shows that for the Q 1 rot element on rectangular shape-regular tensor-product meshes, no jump terms are needed to stabilize the method. In this case moreover, for smooth solutions we derive in the streamline-diffusion norm convergence of order h 3/2 (uniformly in the diffusion coefficient of the problem), where h is the mesh diameter. (This estimate is already known for the conforming case.) Our analysis also shows that similar stability and convergence results fail to hold true for analogous piecewise linear nonconforming elements.