Date:

Location:
POT 745
Speaker(s) / Presenter(s):
Charuka Dilhara Wickramasinghe, University of Kentucky
Title: A C0 finite element method for the biharmonic problem with Dirichlet boundary conditions in a polygonal domain
Abstract:
In this talk, we discuss the biharmonic equation with Dirichlet boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the fourthorder problem into a system of two Poison equations and one Stokes equation, or a system of one Stokes equation and one Poisson equation. It is shown that the solution of each system is equivalent to that of the original fourthorder problem on both convex and nonconvex polygonal domains. Two finite element algorithms are in turn proposed to solve the decoupled systems. In addition, we show the regularity of the solutions in each decoupled system in both the Sobolev space and the weighted Sobolev space, and we derive the optimal error estimates for the numerical solutions on both quasiuniform meshes and graded meshes. Numerical test results are presented to justify the theoretical findings.
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