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The FEM will then use variational methods from the calculus of variations to estimate a solution by minimizing a related error function. After which, these simple equations that model the finite elements are then compiled into a larger system of equations that models the entire problem. Thus, to solve the problem, it subdivides a large system into smaller, simpler parts that are called finite elements. The FEM also appraises the unknown function over the domain. Also, the analytical nature of the solutions of these issues typically requires the solution to boundary value problems for PDEs.įurthermore, the FEM formulation of the problem will result in a system of algebraic equations. The FEM generally addresses issues in heat transfer, structural analysis, fluid flow, electromagnetic potential, and mass transport. The finite element method (FEM) is a systematic numerical method for solving problems of engineering and mathematical physics, more specifically PDEs. However, it still requires a more in-depth understanding of what each offer and what your requirements are to make an accurate decision as to which fits your needs. Both methods are similar in the fact that they are systematic numerical methods for solving partial differential equations (PDEs). The majority of the time, one method versus another is dependent on several parameters that uniquely make whichever method you choose, the right fit for your particular circumstances, for example, Finite Element Method (FEM) versus the Finite Volume Method (FVM). However, the term versus still epitomizes the essence of choice. Mainly because I know that there is usually a better way to accomplish a given task, and at the very least, there is a more efficient way of doing it. When I say wisdom, in this case, it is heavily laced with sarcasm. However, whenever there is a preferred method, i.e., one approach versus another, it is usually accompanied by these words of wisdom: “If it ain’t broke, don’t fix it.” This preferred method was somewhat in opposition to another way of approaching a task.
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