CAMS Seminar Speaker – Peimeng Yin (Wayne State University)
Title: A $C^0$ finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain Peimeng Yin Wayne State University Abstract: ZOOM Link: In our work, 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. This is a joint work with Hengguang Li and Zhimin Zhang.