Galerkin finite element method to solve two-dimensional (2D) laplace's equation
Nowadays, most of real world problems in mathematical engineering and physics fields are represented by using Two-Dimensional (20) Laplace's Equation. The best technique to solve Two-Dimensional (2D) Laplace's Equation is by using Finite Element Method. However, the engineers face some...
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| Main Author: | |
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| Format: | Final Year Project Report |
| Language: | English English |
| Published: |
Universiti Malaysia Sarawak, (UNIMAS)
2015
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| Subjects: | |
| Online Access: | http://ir.unimas.my/id/eprint/39077/1/Halimatul%20%2824pgs%29.pdf http://ir.unimas.my/id/eprint/39077/4/Halimatul%20%28fulltext%29.pdf http://ir.unimas.my/id/eprint/39077/ |
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| Summary: | Nowadays, most of real world problems in mathematical engineering and physics fields
are represented by using Two-Dimensional (20) Laplace's Equation. The best technique to solve
Two-Dimensional (2D) Laplace's Equation is by using Finite Element Method. However, the
engineers face some problem as the Finite Element Method is designed specifically for a certain
problem and hardly to be implemented for other related problem. This is because the current
solution of Finite Element Method is not in general equation. Most of the solutions have applied
the additional variable into the main equation of Finite Element Method based on their problem
fields, thus the solution with general equation of Finite Element Method does not exist. Since
each problem field has different additional variable needed, it becomes the reason that the
current solution of Finite Element Method hardly be used by the engineers to solve problem from
different fields. Therefore, this project is trying to develop a solution with general equation of
Finite Element Method by using Galerkin technique in order to solve Two-Dimensional (20)
Laplace's Equation. This proposed method is the combination of Finite Element Method and
Galerkin technique, where the existing solution of Finite Element Method is modified to
correspond with Galerkin technique. From the general equation of Galerkin Finite Element
Method obtained, engineers can use the same basic equation of Finite Element Method to solve
Two-Dimensional (20) Laplace's Equation and only consider additional variable needed to
correspond with their different problem fields. |
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