论文标题
四曲曲线奇异扰动问题的强大混合有限元方法
Robust mixed finite element methods for a quad-curl singular perturbation problem
论文作者
论文摘要
为Quad-Curl单数扰动问题开发了可靠的混合有限元方法。较低阶H（毕业卷） - 不结合，但H（curl）合并有限元元素被构造为不合格的有限元stokes confffectes和相关的交换图。然后，使用H（毕业卷） - 符合有限元来离散Quad-Curl单数扰动问题，该问题具有相对于扰动参数的清晰且均匀的误差估计。利用Nitsche的技术来实现边界层的最佳收敛速率。提供数值结果以验证理论收敛速率。此外，确定了四曲曲线奇异扰动问题的规律性。
Robust mixed finite element methods are developed for a quad-curl singular perturbation problem. Lower order H(grad curl)-nonconforming but H(curl)-conforming finite elements are constructed, which are extended to nonconforming finite element Stokes complexes and the associated commutative diagrams. Then H(grad curl)-nonconforming finite elements are employed to discretize the quad-curl singular perturbation problem, which possess the sharp and uniform error estimates with respect to the perturbation parameter. The Nitsche's technique is exploited to achieve the optimal convergence rate in the case of the boundary layers. Numerical results are provided to verify the theoretical convergence rates. In addition, the regularity of the quad-curl singular perturbation problem is established.
