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Several methods are developed for the numerical solution of partial differential equations, namely, meshed-solution methods such as the finite-element method (FEM), finite-difference method, and boundary-element method; and numerical algorithms consisting of so-called meshed-solution methods. This article introduces the methods of so-called meshed solutions, with an emphasis on the FEM. It presents some basic differential equations that are used to model the responses of structures, components, processes, or systems with emphasis on continuum mechanics. The article provides an outline on the mathematical principles of solving differential equations. It also reviews linear structural problems to illustrate the concept of the FEMs.

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Modeling with the Finite-Element Method, Fundamentals of Modeling for Metals Processing, Vol 22A, ASM Handbook, Edited By D.U. Furrer, S.L. Semiatin, ASM International, 2009, p 34–54,

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