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A new low order least squares nonconforming characteristics mixed finite element method for Burgers' equation

机译：Burgers方程的一种新的低阶最小二乘非协调特征混合有限元方法

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摘要

In this paper, a new low order least squares nonconforming characteristics mixed finite element method (MFEM) is considered for two-dimensional Burgers' equation. By use of two typical characters of the elements for approximating the velocity and flux variables: (a) the consistency errors of the elements can be estimated as order O(~(h2)) with respect to the mesh size h in the broken ~(H1)-norm, one order higher than their interpolation errors; (b) the elements' interpolation operators satisfy certain orthogonalities, which lead to O(~(h2)) order error estimates in ~(L2)-norm and some superclose results, the accuracy of corresponding variables in ~(L2)-norm is improved by one order compared with other MFEMs in the existing literature. It seems that the results provided herein have never been derived before.
机译：本文针对二维Burgers方程，考虑了一种新的低阶最小二乘不符合特征混合有限元方法（MFEM）。通过使用元素的两个典型特征来近似速度和通量变量：（a）元素的一致性误差可以估计为相对于破碎的〜（）中网格尺寸h的阶次O（〜（h2））。 H1）范数，比其内插误差高一阶; （b）元素的插值算子满足一定的正交性，导致〜（L2）-范数中的O（〜（h2））阶次误差估计和一些超闭合结果，〜（L2）-范数中相应变量的精度为与现有文献中的其他MFEM相比，改进了一个顺序。似乎本文提供的结果以前从未得出过。

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