What is Finite: Definition and 1000 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. Math Amateur

    MHB Finite Integral Domains .... Adkins & Weintraub, Proposition 1.5 ....

    I am reading "Algebra: An Approach via Module Theory" by William A. Adkins and Steven H. Weintraub ... I am currently focused on Chapter 2: Rings ... I need help with an aspect of the proof of Proposition 1.5 ... ... Proposition 1.5 and its proof read as...
  2. Math Amateur

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  3. D

    MHB Proving Finite subgroups of the multiplicative group of a field are cyclic

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  4. P

    I How is the universe expanding if the speed of light is finite?

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  5. T

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  6. Jason Louison

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  7. C

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  8. nomadreid

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  9. mertcan

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  10. lfdahl

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  11. L

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  12. E

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  13. M

    A Is the discretization for the PDE correct?

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  14. M

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  15. B

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  16. RJLiberator

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  17. L

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  18. P

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  19. B

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  20. mertcan

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  21. O

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  22. A

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  23. lfdahl

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  24. L

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  25. H

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  26. W

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  27. B

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  28. J

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  29. Jason Louison

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  30. Shakattack12

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  31. maistral

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  32. Math Amateur

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  33. Math Amateur

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  34. M

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  35. D

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  36. F

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  37. Math Amateur

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  38. Math Amateur

    I Existence and Uniqeness of Finite Fields ....

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  39. Y

    MHB Partial Order Relation where the Set is not Necessarily Finite

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  40. F

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  41. F

    Understanding Finite Element Method: Diagonal Values and Calculating K Matrix

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  42. Math Amateur

    MHB Confirm/Critique Solution to Dummit and Foote, Section 13.2: Exercise 2

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  43. Math Amateur

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  44. Math Amateur

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  45. Wendel

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  46. maistral

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  47. maistral

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  48. R

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  49. ShayanJ

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  50. A

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