论文标题
第四阶椭圆形奇异扰动问题的Morley-Wang-XU元素方法
A Morley-Wang-Xu element method for a fourth order elliptic singular perturbation problem
论文作者
论文摘要
对于第四阶椭圆奇异的扰动问题，提出了一种具有简单修改右侧的Morley-Wang-XU（MWX）元素方法，其中离散双线性形式是标准的，照常不合格的有限元方法。此MWX元素方法给出了急剧误差分析。在边界层的情况下，将Nitsche的技术应用于MXW元素方法，以达到最佳收敛速率。 MWX元素方法的一个重要特征是对求解器友好。基于离散的Stokes复合物在二维中，MWX元素方法被解耦为一个Lagrange元素方法的Poisson方程方法，两种Morley元素泊松方程的方法和一个不合格的$ P_1 $ - $ P_0 $ - $ P_0 $元素方法，这意味着对MWX元素方法的有效和鲁棒性溶液方法。提供了一些数值示例来验证理论结果。
A Morley-Wang-Xu (MWX) element method with a simply modified right hand side is proposed for a fourth order elliptic singular perturbation problem, in which the discrete bilinear form is standard as usual nonconforming finite element methods. The sharp error analysis is given for this MWX element method. And the Nitsche's technique is applied to the MXW element method to achieve the optimal convergence rate in the case of the boundary layers. An important feature of the MWX element method is solver-friendly. Based on a discrete Stokes complex in two dimensions, the MWX element method is decoupled into one Lagrange element method of Poisson equation, two Morley element methods of Poisson equation and one nonconforming $P_1$-$P_0$ element method of Brinkman problem, which implies efficient and robust solvers for the MWX element method. Some numerical examples are provided to verify the theoretical results.
