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lukejo
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i need a full explanation on finite element method or better still a material i can read to help me understand better
The finite element method (FEM) is a numerical technique used to solve problems in engineering and applied sciences. It involves dividing a complex structure or system into smaller, simpler elements, and using mathematical equations to approximate the behavior of each element. These equations are then solved to obtain an overall solution for the entire system.
The finite element method offers several advantages over traditional analytical methods, such as the ability to handle complex geometries and boundary conditions, and the ability to model nonlinear behavior. It also allows for more accurate and efficient solutions for problems with large numbers of variables.
The finite element method is widely used in various fields, such as structural engineering, mechanical engineering, and fluid mechanics. It is used to analyze and design structures such as buildings, bridges, and aircraft, as well as to model fluid flow and heat transfer in industrial processes.
One limitation of the finite element method is that it relies on simplifying assumptions and approximations, which may lead to errors in the results. It also requires a significant amount of computational resources and expertise to properly implement and interpret the results.
The finite element method differs from other numerical methods, such as finite difference method and finite volume method, in its approach to discretization. FEM divides the problem domain into elements, while finite difference method divides it into grid points, and finite volume method divides it into control volumes. FEM also allows for more flexibility in modeling complex geometries and boundary conditions compared to other methods.