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. T

    What are the limitations of the Explicit Finite Difference Model?

    Homework Statement:: Discuss the limitation of the Explicit Finite Difference Model. Relevant Equations:: no formula Hello there, I have to discuss the limitations of using the Explicit Finite Difference model to calculate a 2D Heat Diffusion through an aluminium place, however, I really...
  2. T

    Finite Square Well, Ψ[SUB]III[/SUB] const related too Ψ[SUB]II[/SUB]?

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  3. kmm

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  4. I

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  5. D

    A Numerical Hartree Fock with Finite Difference Matrices for Helium

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  6. F

    Vector space of functions from finite set to real numbers

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  7. J

    I Decomposition per the Fundamental Theorem of Finite Abelian Groups

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  8. A

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  9. K

    I Finite fields, irreducible polynomial and minimal polynomial theorem

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  10. jaketodd

    I Equation for Gravity Going to Zero at Finite Distance?

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  11. L

    I Symbol for Finite: Exploring the Use and Interpretation of ##<\infty##

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  12. P

    MHB Exploring Finite Group Theory: Finding the Upper Bound of Groups of Order

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  13. Terrycho

    I The wave function in the finite square well

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  14. dk123

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  15. E

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  16. evinda

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  17. W

    Engineering Derivation of the error due to a finite load attached to a potentiometer

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  18. jeremiahrose99

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  19. D

    Finite rotations and infinitesimal rotations

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  20. TopologyisGeometry

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  21. P

    Engineering Finite Element Analysis / Structural Analysis

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  22. I

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  23. C

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  24. L

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  25. R

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  26. K

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  27. C

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  28. L

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  29. L

    A Representations of finite groups -- Equivalent representations

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  30. T

    Abuse of the Finite Element Method

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  31. Saptarshi Sarkar

    I Effects of photons having a finite mass

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  32. S

    B Exploring the Finite Universe Concept: Insights from the Big Bang Theory

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  33. T

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  34. Ehyeh Asher Ehyeh

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  35. Haynes Kwon

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  36. R

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  37. Telemachus

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  38. J

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  39. C

    MHB Finite vs Ring Groups: Examining Theorems

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  40. Yalanhar

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  41. I

    Simple Finite Square Well Problem help *Ignore, made stupid mistake*

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  42. Philip Koeck

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  43. M

    I What if the Jacobian doesn't exist at finite points in domain of integral?

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  44. H

    Nonlinear Structural Analysis with Finite Element Method

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  45. patrykh18

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  46. Buzz Bloom

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  47. E

    B Finite & Infinite: Univerally Accepted Definitions?

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  48. nomadreid

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  49. Shackleford

    PhD in Applied Mathematics - Finite Element Analysis

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  50. mertcan

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