๐๐๐ฉ๐๐ค๐๐จ ๐ค๐ ๐ผ๐ฃ๐๐ก๐ฎ๐จ๐๐จ The finite element method (FEM) is a widely used method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a particular numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain.[1] The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. The FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.
๐๐๐๐ง๐ ๐๐ง๐ ๐ฉ๐ฌ๐ค ๐ข๐๐๐ฃ ๐ฉ๐ฎ๐ฅ๐๐จ ๐ค๐ ๐ข๐๐ฉ๐๐ค๐ ๐๐ฃ๐๐ก๐ฎ๐จ๐๐จ:-
- Qualitative Analysis. This approach mainly answers questions such as 'why,' 'what' or 'how. ...
- Quantitative Analysis. Generally, this analysis is measured in terms of numbers. ...
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