Browsing by Author "Mohammed, Taha Yousif Mohammed"
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Item FINITE ELEMENT SOLUTION OF THE POISSON EQUATION(2022-02-15) Mohammed, Taha Yousif Mohammed; Eid, RajehThe finite element method (FEM) has been implemented in this thesis to solve the two dimensional (2D) Poisson equation (see [9]). We used the shape function procedure to construct our algorithm. The shape function considered in this study employs two types of interpolation functions, which are linear and quadratic shape functions (see [2] and [10]). We made use of linear shape function on 3-node triangular elements and 4-node rectangular elements, while the quadratic shape function has been used on 6- node triangular and rectangular elements. Then we applied the finite element method to compute the approximate solution of the problem under consideration. Numerical experiments were performed for both linear and quadratic shape functions to show the accuracy of the solution. The efficiency of the method has been observed by comparing the numerical results obtained by using finite element method with the exact solution.