论文标题
不合格的有限元近似值和Nitsche在三个维
Nonconforming finite element approximations and the analysis of Nitsche's method for a singularly perturbed quad-curl problem in three dimensions
论文作者
论文摘要
我们介绍并分析了三维奇异扰动的四维四维元素模型问题的强大不合格有限元方法。对于模型问题的解决方案，我们得出了适当的先验边界，基于该界限，我们证明所提出的有限元方法相对于单数扰动参数$ \ varepsilon $是可靠的，并且数值解决方案与$ h^{1/2} $均匀收敛。此外，我们研究了通过Nitsche方法弱处理第二个边界条件的效果。我们表明，这种处理会导致误差估计比在参数$ \ varepsilon <h $时强烈施加边界条件。最后，提供了数值实验来说明该方法的良好性能并确认我们的理论预测。
We introduce and analyze a robust nonconforming finite element method for a three dimensional singularly perturbed quad-curl model problem. For the solution of the model problem, we derive proper a priori bounds, based on which, we prove that the proposed finite element method is robust with respect to the singular perturbation parameter $\varepsilon$ and the numerical solution is uniformly convergent with order $h^{1/2}$. In addition, we investigate the effect of treating the second boundary condition weakly by Nitsche's method. We show that such a treatment leads to sharper error estimates than imposing the boundary condition strongly when the parameter $\varepsilon< h$. Finally, numerical experiments are provided to illustrate the good performance of the method and confirm our theoretical predictions.
