Date of Award
8-2023
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
School of Mathematical and Statistical Sciences
Committee Chair/Advisor
TImo Heister
Committee Member
Fei Xue
Committee Member
Leo Rebholz
Abstract
Partial differential equations are frequently utilized in the mathematical formulation of physical problems. Boundary conditions need to be applied in order to obtain the unique solution to such problems. However, some types of boundary conditions do not lead to unique solutions because the continuous problem has a null space. In this thesis, we will discuss how to solve such problems effectively. We first review the foundation of all three problems and prove that Laplace problem, linear elasticity problem and Stokes problem can be well posed if we restrict the test and trial space in the continuous and discrete finite element setting. Next, we introduce methods to solve the linear system and obtain a numerical solution.Finally, we will present the numerical experiments conducted in the finite element library deal.II. We compare the numerical and graphical output to evaluate the performance of each method, providing a more comprehensive understanding of the strengths and limitations.
Recommended Citation
Jia, Pengfei, "Null Space Removal in Finite Element Discretizations" (2023). All Theses. 4090.
https://open.clemson.edu/all_theses/4090
Author ORCID Identifier
C73956030
Included in
Numerical Analysis and Computation Commons, Other Applied Mathematics Commons, Partial Differential Equations Commons