Developing efficient finite element methods for nonlocal PDEs
Nonlocal partial differential equations (PDE) are used to model phenomena in many fields like physics and chemistry. These models require high computational power and are difficult to solve. The purpose of this thesis is to develop efficient finite element methods for nonlocal heat and wave equation...
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Nanyang Technological University
2023
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sg-ntu-dr.10356-1721112023-11-27T15:35:46Z Developing efficient finite element methods for nonlocal PDEs Wang, Jeremy Zhi Zhong Wang Li-Lian School of Physical and Mathematical Sciences LiLian@ntu.edu.sg Science::Mathematics::Applied mathematics::Numerical analysis Nonlocal partial differential equations (PDE) are used to model phenomena in many fields like physics and chemistry. These models require high computational power and are difficult to solve. The purpose of this thesis is to develop efficient finite element methods for nonlocal heat and wave equations with Dirichlet boundary conditions. In this thesis, the Galerkin finite element method is used to get numerical solutions for the PDEs, and the Crank-Nicolson method is used for time discretisation. The errors for each nonlocal PDE are shown and a plot of numerical solutions is shown. The results show that the finite element can be used to efficiently model nonlocal PDEs and the errors are approximately O(h^2). Bachelor of Science in Mathematical Sciences 2023-11-27T02:39:15Z 2023-11-27T02:39:15Z 2023 Final Year Project (FYP) Wang, J. Z. Z. (2023). Developing efficient finite element methods for nonlocal PDEs. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/172111 https://hdl.handle.net/10356/172111 en application/pdf Nanyang Technological University |
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Science::Mathematics::Applied mathematics::Numerical analysis Wang, Jeremy Zhi Zhong Developing efficient finite element methods for nonlocal PDEs |
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Nonlocal partial differential equations (PDE) are used to model phenomena in many fields like physics and chemistry. These models require high computational power and are difficult to solve. The purpose of this thesis is to develop efficient finite element methods for nonlocal heat and wave equations with Dirichlet boundary conditions. In this thesis, the Galerkin finite element method is used to get numerical solutions for the PDEs, and the Crank-Nicolson method is used for time discretisation. The errors for each nonlocal PDE are shown and a plot of numerical solutions is shown. The results show that the finite element can be used to efficiently model nonlocal PDEs and the errors are approximately O(h^2). |
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Wang Li-Lian |
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Wang Li-Lian Wang, Jeremy Zhi Zhong |
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Final Year Project |
author |
Wang, Jeremy Zhi Zhong |
author_sort |
Wang, Jeremy Zhi Zhong |
title |
Developing efficient finite element methods for nonlocal PDEs |
title_short |
Developing efficient finite element methods for nonlocal PDEs |
title_full |
Developing efficient finite element methods for nonlocal PDEs |
title_fullStr |
Developing efficient finite element methods for nonlocal PDEs |
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Developing efficient finite element methods for nonlocal PDEs |
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developing efficient finite element methods for nonlocal pdes |
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Nanyang Technological University |
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2023 |
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https://hdl.handle.net/10356/172111 |
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