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Author:

Zheng, Bin

Title:

Finite Element Approximations of High Order Partial Differential Equations

Graduate Program:

Mathematics

Keywords:

finite element methods
high order partial differential equations
magnetohydrodynamics

File:

Download mythesis.pdf

Committee Members:

Jinchao Xu, Committee Chair/Co-Chair
Chun Liu, Committee Member
Eric M Mockensturm, Committee Member
Victor Nistor, Committee Member
Ludmil Tomov Zikatanov, Committee Member

Author:

Cho, Durkbin

Title:

MULTILEVEL METHODS FOR THE GENERALIZED FINITE ELEMENT METHOD DISCRETIZATIONS

Graduate Program:

Mathematics

Keywords:

Generalized finite element method
Subspace correction methods
Auxiliary space methods
Multilevel methods
Exact controllability technique

File:

Download mythesis.pdf

Committee Members:

Ludmil Tomov Zikatanov, Committee Chair/Co-Chair
Jinchao Xu, Committee Member
Victor Nistor, Committee Member
Virendra Puri, Committee Member

Author:

Xue, Guangri

Title:

Numerical Methods for Multiphysics, Multiphase, and Multicomponent Models for Fuel Cells

Graduate Program:

Mathematics

Keywords:

Numerical methods
multiphysics
multicomponent
fuel cell
multiphase
coupling

File:

Download thesis-GuangriXue.pdf

Committee Members:

Jinchao Xu, Committee Chair/Co-Chair
Ludmil Tomov Zikatanov, Committee Member
Chun Liu, Committee Member
Alberto Bressan, Committee Member
Chao Yang Wang, Committee Member

Author:

Sun, Huan

Title:

AN ENERGETIC VARIATIONAL APPROACH TO MODELING COMPLEX FLUIDS AND ITS NUMERICAL SIMULATIONS

Graduate Program:

Mathematics

Keywords:

PDE
variational techniques
complex fluids
numerical simulations

File:

Download thesis_main.pdf

Committee Members:

Chun Liu And James Brannick, Dissertation Advisor/Co-Advisor
Chun Liu, Committee Chair/Co-Chair
James Joseph Brannick, Committee Chair/Co-Chair
Xiantao Li, Committee Member
Yuxi Zheng, Committee Member
Ludmil Tomov Zikatanov, Committee Member
Ralph H Colby, Committee Member

Author:

Li, Hengguang

Title:

ELLIPTIC EQUATIONS WITH SINGULARITIES: A PRIORI ANALYSIS AND NUMERICAL APPROACHES

Graduate Program:

Mathematics

Keywords:

the finite element method
weighted sobolev spaces
singularities
elliptic equations
a priori analysis
the multigrid method

File:

Download HengguangLiDissertation.pdf

Committee Members:

Victor Nistor, Committee Chair/Co-Chair
Ludmil Tomov Zikatanov, Committee Chair/Co-Chair
Jinchao Xu, Committee Member
Anna L Mazzucato, Committee Member
Corina Stefania Drapaca, Committee Member

Author:

Wang, Jiakou

Title:

STOCHASTIC AND DETERMINISTIC COAGULATION MODELS, THEIR NUMERICAL APPROXIMATIONS AND APPLICATIONS TO CELL AGGREGATION

Graduate Program:

Mathematics

Keywords:

cell aggregation
coagulation equation
stochastic model
time relaxed method

File:

Download Wang-Dissertation.pdf

Committee Members:

Qiang Du, Committee Chair/Co-Chair
Cheng Dong, Committee Member
Chun Liu, Committee Member
Suzanne Michelle Shontz, Committee Member
Ludmil Tomov Zikatanov, Committee Member

Author:

Pan, Jia

Title:

OPTIMAL INTERMEDIATED INVESTMENT IN A LIQUIDITY-DRIVEN BUSINESS CYCLE

Graduate Program:

Mathematics

Keywords:

dynamical programming
general equilibrium
infinite horizon
liquidity risk
banking
numerical algorithm

File:

Download mythesis.pdf

Committee Members:

Edward James Green, Committee Chair/Co-Chair
Jenny Li, Committee Chair/Co-Chair
Qiang Du, Committee Member
Ludmil Tomov Zikatanov, Committee Member
Ruilin Zhou, Committee Member

Author:

Chen, Long

Title:

Robust and Accurate Algorithms for Solving Anisotropic Singularities

Graduate Program:

Mathematics

Keywords:

mesh adaptation
anisotropic error estimate
convection dominated problem
singularly perturbed problem
optimal Delaunay triangulation
nonlinear approximation

File:

Download MyThesis.pdf

Committee Members:

Jinchao Xu, Committee Chair/Co-Chair
Qiang Du, Committee Member
Chun Liu, Committee Member
James Z Wang, Committee Member
Ludmil Tomov Zikatanov, Committee Member

Author:

Zhang, Lei

Title:

Phase field model for the nucleation in solid state phase transformations: Theories, Algorithms and Applications

Graduate Program:

Mathematics

Keywords:

Phase field
nucleation
critical nucleus
solid state

File:

Download Lei-Dissertation.pdf

Committee Members:

Qiang Du, Dissertation Advisor/Co-Advisor
Qiang Du, Committee Chair/Co-Chair
Long Qing Chen, Committee Member
Chun Liu, Committee Member
Ludmil Tomov Zikatanov, Committee Member
Xiantao Li, Committee Member

Author:

Emelianenko, Maria

Title:

Multilevel and Adaptive Methods for Some Nonlinear Optimization Problems

Graduate Program:

Mathematics

Keywords:

optimization
multigrid methods
computational geometry
numerical analysis
computational methods in materials science

File:

Download emelianenko-Dissertation.pdf

Committee Members:

Qiang Du, Committee Chair/Co-Chair
Ludmil Tomov Zikatanov, Committee Member
Dr Zi Kui Liu, Committee Member
Dr Hongyuan Zha, Committee Member
Wen Shen, Committee Member
Nigel David Higson, Committee Member