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The beginnings of the finite element method actually stem from these early numerical methods and the frustration associated with attempting to use finite difference methods on more difficult, geometrically irregular problems. The solution domain is discretized into individual elements – these elements are operated upon individually and then solved globally using matrix solution techniques.Įarly work on numerical solution of boundary-valued problems can be traced to the use of finite difference schemes South well used such methods in his book published in the mid 1940’s.
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The FEM has been used to solve a wide range of problems, and permits physical domains to be modeled directly using unstructured meshes typically based upon triangles or quadrilaterals in 2-D and tetrahedrons or hexahedrals in 3-D. The FEM utilizes the method of weighted residuals and integration by parts (Green-Gauss Theorem) to reduce second order derivatives to first order terms.
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The method is based on the integration of the terms in the equation to be solved, in lieu of point discretization schemes like the finite difference method.
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The FEM is a novel numerical method used to solve ordinary and partial differential equations.
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