Finite Definition and 1000 Threads

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

    Can anyone think of an example of an infinite group that has elements with a finite order?
  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

    Homework Statement This is primarily a question that I'm trying to program into python. I want to know the potential at some distance (x,y) from the center of a square plane. Homework Equations V = integral (k/r) dq The Attempt at a Solution The way I see this mathematically is a...
  9. L

    Help with finite difference for matlab

    I have a question which states that I have to solve Phi using the finite difference method in matlab. Phi = Phi_infinity - Phi_t where Phi_infinity = 1 - e^2 and Phi_t = A(t).B(e) A has the differential for dA/dt = -c^2. A and B 1/e.d/de(edB/de)=-c^2.B where e is a separation...
  10. jegues

    Striaght Line Charge of Finite Length (E Field)

    Straight Line Charge of Finite Length (E Field) Homework Statement Find the expression for the E field at an arbitrary point in space due to a straight line of length l uniformly charged with total charge Q. The ambient medium is air. Homework Equations The Attempt at a Solution...
  11. C

    What's is dv for a finite cylinder?

    For an infinite cylinder dV=2*pi*r*L*dr Would dv=pi*L*r*dr for a finite cylinder?
  12. M

    HELP with finite element homework

    Homework Statement Two ends of a bar of length L are held at temperatures To and TL at positions x=o and x=L, respectively. Thermal conductivity k(x)= Ko/(1+ x/L) , ko is a constant. cross section of the bar is uniform and longs sides are thermally insulated, there's no source of heat...
  13. T

    Wavelength in finite potential well

    Homework Statement 1)The graph below represents the ground state wave function of an electron in a finite square well potential of width L. The potential is zero at x = 0. The wave function of the electron within the well is of the form A cos( 2πx / λ ) where A is a normalization...
  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

    Homework Statement I just took an exam and one of the questions gave us a finite line of charge and asked us to calculate the E-field at a point at a point P to the right of the line of charge. here is a poor sketch [+][+][+][+][+][+][+][+][+][+][+][+]---------------------------------- .P...
  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

    Homework Statement For a given function u=u(x,t), start with Taylor series to implement the forward finite difference method to the heat conduction equation in non-dimensional form \frac{\partial u}{\partial t}=\frac{\partial ^2u}{\partial x^2} by using the following steps: a)...
  18. M

    Value of fracture toughness for a finite plate

    Hiii heeeeeelp please. I am new here and hope to find a solution and an easy to understand explanation to my problem:confused:. Thank you all :smile: a. A specimen corresponding to a finite plate of width W = 65 mm is made from a steel with a yield strength of 650 MN m^-2 and contains an edge...
  19. F

    Function composition in finite differences

    Hi. I am trying to express the following in finite differences: [ tex ] \frac{d}{x}\left[ A(x)\frac{d\, u(x)}{x} \right] [ /tex ] If I take centered differences I get: [ tex ] \left{ \frac{d}{x}\left[ A(x)\frac{d\, u(x)}{x} \right] \right}_i = \frac{[A(x)\frac{d\, u(x)}{x}]_{i+1/2} -...
  20. A

    A Singularity: Finite Function, Infinite Derivatives

    Hi, Do you know the name of this kind of singularity at A ? The function is finite but the left derivative is +\infty and the right derivative is -\infty. http://shareimage.org/viewer.php?file=mt79897bbpxxse1v8pzb.jpg Thanks
  21. B

    Corollaries of the Theorem of Finite Abelian Groups

    Homework Statement If G is a finite abelian group and p is a prime such that p^n divides order of G, then prove that G has a subgroup of order p^n Homework Equations Theorem of Finite Abelian Groups: Every finite abelian group G is a direct sum of cyclic groups, each of prime power...
  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

    As I understand Energy is finite. This is a problem for me tho as I can see one way to create energy. In fact in my eyes energy is created everyday in are very own solar system. Anyway I want to get some points of view on the subject from others before I make my self a fool because maybe you...
  24. 8

    Finite Fields Homework: Showing K has q Elements

    Homework Statement Let q=pm and let F be a finite field with qn elements. Let K={x in F: xq=x} (a) Show that K is a subfield of F with at most q elements. (b) Show that if a and b are positive integers, and a divides b, then Xa-1 divides Xb-1 i. Conclude that q-1 divides...
  25. R

    Finite element method/crumple zones

    I'm looking for information regarding the use of the finite element method (FEM) for crash test analysis and crumple zones? Basically I'm wondering what part of FEM do I use to make crash test analysis possible. I'm also looking for books on the subject or software libraries that can be used for...
  26. S

    Representation of a finite group

    Homework Statement Prove that a representation of a finite group G is faithful if and only if its image is isomorphic to G. Homework Equations The Attempt at a Solution
  27. M

    Brane world with finite thickness

    In most of the brane world models: our world is supposed to be an infinite thick mathematical surface in the higher dimensional world. Which is very curious. Are there any model in which the thickness of the "surface" is finite? Please, could anyone submit a good paper to me in this topic?
  28. M

    Stargazing Why Not Leave Hubble in Space Until It Fails?

    Hey, not sure if this is the correct forum but it seems physics will ultimately bring down the telescope. Why can't we leave the Hubble in space until it doesn't work anymore? It doesn't have any space crew to kill, it would break up on re-entree harming no-one and would continue to inspire our...
  29. R

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

    This may not be the correct Forum to post this Thread, but i thought i might as well. I was just wondering: if the matter in the Universe is assumed to be 13.75 billions years old, why is it that we can witness things over 13.75 billion light years away? I came across this Wikipedia article on...
  30. N

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

    Circuler grid need to be solved by Finite difference method! pls help me... hi this is the picture of the problem.. i have studied the rectangular grid but not the circular grid... now pls someone help me to find out the way to solve a heat conduction problem for circle using finite difference...
  31. M

    Estimation of residual stress by finite element analysis

    I am trying to do a finite element analysis ofcold extrusion process of a tube wherein the steel tube is reduced from a larger outer diamter to a smaller one by extrusion process.The tube is held stationary and the die is pushed into the tube for a particular length and then retrieved.I am...
  32. Z

    Show that x(t) approaches infinity in finite time

    Homework Statement Consider the equation \dot{x} = rx + x^3, where r>0 is fixed. Show that x(t) \rightarrow \pm \infty in finite time, starting from any initial condition x_{0} \neq 0. Homework Equations I can think of none. The Attempt at a Solution The idea alone of x(t) approaching...
  33. K

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

    Why must a polynomial be finite in length? Is there such thing as a recursive polynomial? Thanks guys!
  34. Z

    Topology question: finite sets

    Homework Statement If A and B are finite, show that the set of all functions f: A --> B is finite. Homework Equations finite unions and finite caretesian products of finite sets are finite The Attempt at a Solution If f: A -> B is finite, then there exists m functions fm mapping to...
  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

    Is it true that any linear map between two arbitrary finite-dimensional vector spaces is continuous? Is it differentiable?
  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?

    Continue reading...
  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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