论文标题
$ c^0 $有限元法，用于多边形域中的Navier边界条件的Biharmonic问题
A $C^0$ finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain
论文作者
论文摘要
在本文中，我们研究了多边形结构域中Navier边界条件的Biharmonic方程。特别是，我们提出了一种有效地将四阶问题解散到泊松方程系统的方法。与导致两个泊松问题的通常混合方法不同，但仅适用于凸域，所提出的分解涉及第三个泊松方程，以将溶液限制在正确的函数空间中，因此可以在凸和非convex域中使用。 A $ C^0 $有限元算法又提出了解决结果系统。此外，我们在准均匀的网格和分级网格上得出了数值解的最佳误差估计。提出了数值测试结果以证明理论发现合理。
In this paper, we study the biharmonic equation with the Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the 4th-order problem into a system of Poisson equations. Different from the usual mixed method that leads to two Poisson problems but only applies to convex domains, the proposed decomposition involves a third Poisson equation to confine the solution in the correct function space, and therefore can be used in both convex and non-convex domains. A $C^0$ finite element algorithm is in turn proposed to solve the resulted system. In addition, we derive the optimal error estimates for the numerical solution on both quasi-uniform meshes and graded meshes. Numerical test results are presented to justify the theoretical findings.
