Finite Element Method
The finite element method (FEM) is currently one of the most efficient and universal methods of numerical calculation for solving partial differential equations from engineering and scientific fields. The basic mathematical concepts are based on the work of Ritz, Galerkin, Trefftz and others at the beginning of the twentieth century. With the advance of modern computer science in the 1960s, these approaches of numerical solution could be successfully implemented with FEM. This development was motivated to an enormous extent by tasks of structural analyses in aviation, construction and mechanical engineering. The formulation of the finite element method in its current standard was developed thanks to the pioneer work of (among others) Argyris, Zienkiewicz, Turner, and Wilson. Therein, the system of differential equations is converted into an equivalent variational problem (weak formulation), mostly utilizing mechanical principles or weighted residual methods.
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