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. S

    Finite Difference Schemes in Matlab

    Homework Statement This is for a course in numerical solutions of PDEs. So far it has all been theory of PDEs which is great since I am the worst programmer in the world. Right now I have to program the following: to solve the simplest hyperbolic equation, du/dt = du/dx, using the...
  2. P

    Oppenheimer Snyder Collapse - finite time?

    The Oppenheimer Snyder Collapse into a black hole does it happen in finite time for local and remote observers? Does a trapped surface really form in finite time?
  3. H

    Analysis of Finite Square Potential Well: Bound and Scattering States

    Hello, can anyone explain the full analysis of finite square potential well (bound state and scattering state) if V(x) = -Vo, x <= 0 (region 1) V(x) = 0, 0 < x < a (region 2) V(x) = -Vo, x >= a (region 3) It will be helpful if you can attach the analysis in .pdf format. Thank you in...
  4. Z

    Finite square quantum well - depth

    Homework Statement Find the condition on the depth of the finite square well such that one finds two even and one odd bound state energy eigenstates, but no other bound state solutions exist. Your answer should appear as a range of allowed well depths, say ? < Vdepth of well < ? Homework...
  5. M

    Order of elements in finite group

    Homework Statement If G is a finite group such that all elements have prime order(other than the identity). If G has a non-trivial center then show every element has the same order. Homework Equations The Attempt at a Solution Since we know that G has a center, we know that...
  6. E

    Infinite groups with elements of finite order

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  7. B

    Electric Field near a finite conducting stick

    So this should probably go into math's section, but I feel you guys can give me the answer too, since this comes from an EE course(Theory of electromagnetic fields) http://pokit.org/get/2f3e7eef6b38bc75f0023b94976a2997.jpg(1) http://pokit.org/get/fc8658090d67ae0fafe79970021d1518.jpg(2)...
  8. B

    Potential at a Distance away from a FINITE continuously charged plane

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  9. L

    Help with finite difference for matlab

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  10. jegues

    Striaght Line Charge of Finite Length (E Field)

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  11. C

    What's is dv for a finite cylinder?

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  12. M

    HELP with finite element homework

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  13. T

    Wavelength in finite potential well

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  14. D

    Electric potential due to finite rod

    Homework Statement A rod of length L has a total charge Q uniformly distributed along its length. The rod lies along the x-axis with its center at the origin.What is the electric potential as a function of position alon gthe x-axis for x>L/2 Homework Equations V=∫kdq/r = ∫kQ/r dx I'll...
  15. J

    Electric Field of a finite line of charge

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  16. R

    Taylor series and the forward finite difference method

    Given a partial differential equation, how would one go about implementing the forward finite difference method to the Taylor series?
  17. R

    Forward Finite Differene Method

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  18. M

    Value of fracture toughness for a finite plate

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  19. F

    Function composition in finite differences

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  20. A

    A Singularity: Finite Function, Infinite Derivatives

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  21. B

    Corollaries of the Theorem of Finite Abelian Groups

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  22. K

    Boyle's Law, does it hold true in a non finite container ?

    If a gas will expand to fill the available space (container) does this still hold true if the "container" is the atmosphere? Assuming the gas(es) can escape (either in molecular or in subs - atoms) from the area around the Earth containing our atmosphere this means that the gas is not...
  23. C

    Is Energy Finite? thoughts ideas

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  24. 8

    Finite Fields Homework: Showing K has q Elements

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  25. R

    Finite element method/crumple zones

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  26. S

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  27. M

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  28. M

    Stargazing Hubble telescope, finite life?

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  29. R

    Finite Universe: Light speed and the Earth's distance/time from event

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  30. N

    Circuler grid need to be solved by Finite difference method pls help me

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  31. M

    Estimation of residual stress by finite element analysis

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  32. Z

    Show that x(t) approaches infinity in finite time

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  33. K

    Why must a polynomial be finite in length? Is there such thing as a

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  34. Z

    Topology question: finite sets

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  35. P

    Proving the Infinity of C\B: A Contradiction Method

    If C is an infinite set and B is a finite set then C\B is an infinite set. C\B means the complement of B relative to C Ok so I was thinking of doing this by contradiction. I have Assume C\B is a finite set. Then there exist a function\alpha that is bijective from C\B to Nk for some k...
  36. K

    Probability inside finite square well

    Homework Statement What is the probability, that the particle is in the first third of the well, when it is in the ground state? Homework Equations \Psi(x)=Asin((n*pi)/L) A=(2/L)1/2 The Attempt at a Solution so probablility is related to the wave function by \Psi2 so i...
  37. E

    Infinite Mass and Finite Tension over a pulley

    Homework Statement Two masses hang across a massless, frictionless pulley. As the masses become infinitely large, the tension becomes: Homework Equations F=ma The Attempt at a Solution Can someone please help me understand how two masses suspended over a pulley can...
  38. S

    Show the set of all functions from A to B is finite

    Homework Statement If A and B are finite, show the set of all functions f: A \rightarrow B is finite. Homework Equations Lemma. If A is finite such that |A|=n, then there is a bijective correspondence between A and [n]. *Notation. [n] = \{ 1, ..., n \} The Attempt at a Solution...
  39. A

    Help With Finite Difference Method in Solving Second Order Differenial Equation

    Homework Statement y'' + 3y' + 2y = 0, y(0) = 1, y'(0) = 0 Homework Equations Finite Difference Approximations: y'' = (y(ii+1) - 2y(ii) + y(ii-1))/h^2 y' = (y(ii+1) - y(ii-1))/(2h) where h is the finite difference. The Attempt at a Solution I wrote the MATLAB code (just to try...
  40. N

    Electric Field on finite charged rod

    Homework Statement Thin rod AB has length L=100 cm and total charge q0=37 nC that is distributed in such a way that its line density \lambda is proportional to the square of the distance from the end A, i.e. \lambda(x) =kx^2. Determine electric field E at the end A of the rod. Homework...
  41. A

    Linear maps between finite dimensional spaces

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  42. T

    If the univese is finite will I see my light again.

    As the thread title says, if the universe is finite will i see my light again. I understand that parts of space-time are expanding faster than c, therefore even in a finite yet expanding universe the light will never reach the "boundry". By boundry i mean more of a turning point where the...
  43. O

    Group/Representation Theory Help (Summations and elements of a finite group)

    Apologies, the LaTeX thing doesn't seem to be working, so not very clear! I am working through a book on representation theory, but am stuck on these exercises. Homework Statement Let G be a finite group and let E = Sum g (running over all g in G). (i) Prove: Ex = E (forall x in G)...
  44. D

    Exploring Finite Sets & Limit Points

    Is it true that finite sets don't have limit points?
  45. B

    Irreducible Polynomials over Finite Fields

    Hi, yet another question regarding polynomials :). Just curious about this. Let f(x), g(x) be irreducible polynomials over the finite field GF(q) with coprime degrees n, m resp. Let \alpha , \beta be roots of f(x), g(x) resp. Then the roots of f(x), g(x), are \alpha^{q^i}, 0\leq i \leq n-1...
  46. Greg Bernhardt

    Is the Universe finite, or is it infinite?

    Is the universe finite, or is it infinite? Standard cosmological models come in three flavors, open, flat, and closed,[Carroll] whose spatial curvatures are negative, zero, and positive. The open and flat types have infinite spatial volume. The closed one has finite spatial volume; spatially...
  47. I

    Finite Difference method to solve PDEs

    Hello: I am looking to solve a set of 1D PDEs. I thought the finite difference method would be a good way to go about it. So I decided to pick a simple first order forward difference scheme to obtain preliminary results. I just have 1 question: According to my scheme, at the last node...
  48. D

    Which finite elements are best for structural analysis in engineering courses?

    i am a 3rd year engineering student currently a course in computer methods for structural analysis, as a part of the course we are learning about finite elemnts, we have learned about CST LST Q4 and Q8, but i am having difficulty deciding which element to use for different models. does anyone...
  49. H

    Need A Finite Element Magnetics Code That Handles Dynamic Modeling

    To the EE Forum, I am a new guy on this Physics Forum and this is my first post. I have downloaded a free software code, Finite Element Method Magnetics (FEMM) solver (see http://www.femm.info/wiki/Download) but it doesn’t work because FEMM is limited to solving low frequency electromagnetic...
  50. A

    Understanding Stencils in Finite Difference Methods

    Hi Sorry for the stupid question, but what is exactly a "stencil" in finite difference methods ? Is the results of the expansion points ? Cheers Alex
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