What is Element: Definition and 880 Discussions

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 general 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.
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.
Studying or analyzing a phenomenon with FEM is often referred to as finite element analysis (FEA).

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  1. M

    Conduction - Steady State Triangular Element

    Homework Statement Obtain the temperature distribution T(x,y) of the triangular cross section, assuming constant thermal conductivity, k. The triangle is a right-isosceles triangle with the right angle at (0,0). The triangle goes "up" to a, and to the right to a, then diagonally across...
  2. L

    Evaluating Element Mesh Conformance Criteria

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  3. L

    Exploring the Reactivity of Element 18001: Is It More Powerful Than Cs and Rb?

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  4. C

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  5. S

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  6. M

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  7. M

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  8. S

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  9. Mentz114

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  10. N

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  11. K

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  12. F

    How can I express f*dA in terms of u and v for the given function?

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  13. G

    Making a Coiled Heating Element from Nichrome Wire

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  14. J

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  15. R

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  16. K

    Best Introduction/Fundamentals of Finite Element Methods Texts

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  17. U

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  18. S

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  19. D

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  20. B

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  21. C

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  22. P

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  23. R

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  24. B

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  25. P

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  26. A

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  27. I

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  28. I

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  29. M

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  30. P

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  31. S

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  32. F

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  33. N

    Identifying an element from Emission Spectrum

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  34. J

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  35. C

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  36. J

    How does an atomic element jump the Quantum fence?

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  37. A

    Study Finite Element Methods: Books & Resources

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  38. B

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  39. P

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  40. K

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  41. Astronuc

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  42. R

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  43. K

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  44. E

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  45. B

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  46. C

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  47. C

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  48. M

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  49. B

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  50. M

    How to Find the Half-Life of an Element

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