The finite element method is a method for solving partial differential equations (PDEs). For example a PDE will involve a function u(x) defined for all x in the domain with respect to some given boundary condition. The purpose of the method is to determine an approximation to the function u(x). This method requires the discretisation of the domain into subregions or cells. For example, a two-dimensional domain can be divided and approximated by a set of triangles (the cells). On each cell the function is approximated by a characteristic form. For example u(x) can be approximated by a linear function on each triangle. The method is applicable to a wide range of physical and engineering problems. Finite element method is a powerful technique originally developed for numerical solutions of complex problems in structural mechanics, and it remains the method of choice for complex systems. In FEM, the structural system is modeled by a set of appropriate finite elements interconnected at points called nodes. Elements may have physical properties such as thickness, coefficient of thermal expansion, density, Young's modulus, shear modulus and Poisson's ratio.
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