Galerkin finite element method to solve two-dimensional (2D) laplace's equation

Halimatul Sa'adiah, Ja'ffar (2015) Galerkin finite element method to solve two-dimensional (2D) laplace's equation. [Final Year Project Report] (Unpublished)

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Abstract

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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