PhD Dissertation Defense - Charuka Wickramasinghe

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Date: July 5, 2022
Time: 9:30 a.m. - 10:30 a.m.
Location: Virtual event
Category: Lecture

Speaker:

Charuka Wickramasinghe, PhD Candidate

Title: 

A C0 FINITE ELEMENT METHOD FOR THE BIHARMONIC PROBLEM IN A POLYGONAL DOMAIN

Abstract:

This dissertation studies the biharmonic equation with Dirichlet boundary conditions in a polygonal domain. The biharmonic problem appears in various real-world applications, for example, in plate problems, and in hydrodynamics problems. There are three classical approaches to discretizing the biharmonic equation in the literature: conforming finite element methods, nonconforming finite element methods, and mixed finite element methods. We propose a mixed finite element method that effectively decouples the fourth-order problem into a system of one steady-state Stokes equation and one Poisson equation. As a generalization to the above-decoupled formulation, we propose another decoupled formulation using a system of two Poison equations and one steady-state Stokes equation. It is shown that the solution of each system is equivalent to that of the original fourth-order problem on both convex and non-convex polygonal domains. Two finite element algorithms are, in turn, proposed to solve the decoupled systems. Solving this problem in a non-convex domain is challenging due to the singularity occurring near re-entrant corners. We introduce a weighted Sobolev space and a graded mesh refines algorithm to attack the singularity near re-entrant corners. We show the regularity results of each decoupled system in both Sobolev space and weighted Sobolev space. We derive the H_1 and L_2 error estimates for the numerical solutions on quasi-uniform and graded meshes. We present various numerical test results to justify the theoretical findings.

Zoom Link:

https://wayne-edu.zoom.us/j/9467359355?pwd=QmVYRm1QVzVib29Hb0dIM2JndUt5Zz09

Contact

Department of Mathematics
313-577-2479
math@wayne.edu

Cost

Free
July 2022
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