论文标题
$ p_2 $ - 四阶半连接元素von karman方程的比较结果
Comparison results of $P_2$-finite elements for fourth-order semilinear von Karman equations
论文作者
论文摘要
低阶$ p_2 $有限元元素很受欢迎，可在解决方案有限的规律性有限时求解四阶椭圆PDE。 Carstensen等人考虑了Von Karman方程的先验和后验误差估计。 （2019，2020）关于不同的网格依赖性规范，涉及不同的跳跃和惩罚条款。本文解决了一个问题，它们是否相对于共同规范是可比的。本文确定，二次对称内部不连续的Galerkin的错误，$ C^0 $内部惩罚和不合格的Morley有限元方法相当于相对于统一规范的一些高阶振荡项。进行数值实验以证实比较结果。
Lower-order $P_2$ finite elements are popular for solving fourth-order elliptic PDEs when the solution has limited regularity. A priori and a posteriori error estimates for von Karman equations are considered in Carstensen et al. (2019, 2020) with respect to different mesh dependent norms which involve different jump and penalization terms. This paper addresses the question, whether they are comparable with respect to a common norm. This article establishes that the errors for the quadratic symmetric interior discontinuous Galerkin, $C^0$ interior penalty and nonconforming Morley finite element methods are equivalent upto some higher-order oscillation term with respect to a unified norm. Numerical experiments are performed to substantiate the comparison results.
