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. J

    Is the particle able to penetrate finite barrier?

    Let's have a kind of step potential, V=infinity, where x\leq0, V=constant, where 0\leqx\leqa, V=zero , where x\geqa. Then, my question is that when the energy of the particle is lesser than zero, which means that the particle is in the bound state, is there a probability of getting...
  2. L

    Reducing Normal Subgroup Calcs: Finite Groups Only?

    My abstract algebra book is talking about reducing the calculations involved in determining whether a subgroup is normal. It says: If N is a subgroup of a group G, then N is normal iff for all g in G, gN(g^-1) [the conjugate of N by g] = N. If one has a set of generators for N, it suffices...
  3. T

    Solving a fourth order PDE by finite difference method by matlab

    Homework Statement how can i solve this problem by MATLAB? pls help me A (d4y/dx4) - B(d2y/dt2) = Cy A=E*I B=p*sin(w*t) c=p*w2 conditions are 1.at x=0, dy/dx=0 2.at x=0,y=0 3.at x=L d2y/dx2=0 4. at x=L d3y/dx3=p (p is a function of t here) x=0 and x=L...
  4. N

    Tribology:Numerical solution of finite Journal Bearing-Reynolds condition.

    Hi...:) I need help as to how to solve the Reynolds equation: \partialh/\partialt - \partial((h3/12n)*\partialp/\partialx) - \partial((h3/12n)*\partialp/\partialz) + \partial(U0*h*.5)/\partialx + \partial(W0*h*.5)/\partialz = 0 For a finite journal bearing assuming \partialh/\partialt = 0 And...
  5. Somefantastik

    Finite Set of Points in Complex Plane: $\{e^{n r \pi i}\}$

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  6. I

    Finite Subset Max in Set S: Proof

    Let S be a set on which a linear order <= (less or equal) , is defined. Show that a non-empty finite subset has a max.
  7. Saladsamurai

    1-D Conduction+Convection: eriving a Finite Difference Scheme

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  8. F

    Irreducibility and finite fields

    Trying to do i) and iii) on this past exam paper For part i) I'm pretty stumped I've said that the possible roots of the polynomial are +- all the factors of T In particular rt(T) needs to be a factor of T but this can't be possible? Doesn't sound too good but its the best I've got. Part...
  9. O

    Finding the sum of finite terms of a Maclaurin series

    Homework Statement Hi. Find the sum of the first 10 terms in the series: 1, (ln2)/1!, (ln2)^2/2!, (ln^3)/3!... Homework Equations I guess the Maclaurin series, which is e^k = 1, k/1!, (k^2)/2!, (k^3)/3!... In my case, k = ln2. The Attempt at a Solution I tried to use the sum of the first...
  10. E

    Particle in a box with one finite wall and one infinite wall

    Hello all, I came across what I think is a very interesting question the other day; How would you treat a particle trapped in a square well that had one finite wall and one infinite wall? Say for E[SUB]n[SUB]~(n*pi*(h-bar))2/(2m(L+2d)2) would you replace the 2d by 1d? As you can only find the...
  11. F

    Is Every Subset of a Finite Dimensional Space Also Finite Dimensional?

    Homework Statement How could I prove that the subset of a finite dimensional space is also finite dimensional? Homework Equations N/A The Attempt at a Solution I think it's more intuitive in the sense that since the vector space is finite dimensional the subset is forcibly finite...
  12. I

    Should the state table include the clock and reset button as possible inputs?

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  13. K

    Proving the Unproven: A Finite Ring with Identity

    Let R be a ring with multiplicative identity 1R. Suppose that R is finite. The elemets xy1, xy2,...xyn are all different. So x y_i=1R for some i. A lemma that is not proven is given. If xyi=1R & yjx=1R, then yi=yj I need to show that yjx=1R. Right now I haven't got much. I took...
  14. E

    Particle in finite well (Schroedinger)

    Homework Statement A particle with energy greater than the potential is defined as below: V(x) = Vo (x<0) V(x) = 0 (0<x<a) V(x) = Vo (x>a) a) Write the complete solutions (time and space) to the S. Eqn for the 3 regions b) What condition must the width of the potential satisfy for the...
  15. F

    How Do Numerical and Analytical Solutions Compare in Finite Coulomb Problems?

    Hey guys, I'm doing some numerical solutions to wave equations and i started by checking that my method using NDSolve in mathematica worked by comparing it to the analytic solutions DSolve would produce. Now in terms of numerically solving the schrodinger equation i have done the usual trick to...
  16. K

    Calculating Energy Levels in a Finite Square-Well Potential

    Consider a finite square-well potential well of width 2.8 multiplied by 10-15 m that contains a particle of mass 1.9 GeV/c2. How deep does this potential well need to be to contain three energy levels? (Except for the energy levels, this situation approximates a deuteron. Use the infinite square...
  17. E

    Using Finite Difference Method In Excel

    ------Question------ a) Research the three finite difference approximations mentioned above (forward, backward and central). Use a spreadsheet to demonstrate each of these numerical methods for the function below. y=x3 −x2 +0.5x Investigate the derivative over the range x = [0,1], using...
  18. maverick280857

    MATLAB 2D surface integral in MATLAB for Finite Element Calculation

    Hi everyone, As part of a project, I am required to numerically compute the expression b_{i}^{e} &=& \frac{E_{0}^{i}k_0^2(\epsilon_r-1/\mu_r)}{2\Delta^e}\left[\iint\limits_{\Omega^e}(a_i^e + b_i^e x + c_i^e y)e^{-jk_0 x} dx dy\right] \nonumber\\&&- \frac{jk_0 E_0^i r'}{2\Delta^e...
  19. F

    Finite Abelian Group: Proving # Subgps Order p = # Subgps Index p

    Homework Statement A be a finite abelian group, prove # of subgps of order p = # of subgps of index p, p is a prime. The Attempt at a Solution I have thought about this probably very easy problem for 2 hours and could not find a satisfying proof. I have tried bijective proof but...
  20. K

    Calculating energy for particle in finite box.

    [solved] Calculating energy for particle in finite box. Homework Statement I am going to look at a particle in a finite boxpotential where V(x)=-V0 for -a<x=<a And they are bound, in other words -V0<E<0. This is a transcendtale equation that need to be solved graphicly/numericly. I am aware...
  21. C

    Magnetic Field Around Finite Conductor: Questions & Answers

    Hi everybody... I have a simple question for you.. Where can i found the expression of the magnetic field around at the conductor which it has finite lenght? because i always found the megnetic filed in a conductor infinite length .. Sorry for the stupid question... tanks and best regard
  22. A

    Approximation of boundary value problem using finite differences

    Homework Statement A hot fluid is flowing through a thick-walled cylindrical metal tube at a constant temperature of 450C. The cylinder wall has an inner radius of 1 cm and an outer radius of 2 cm and the surrounding temperature is 20C. The temperature distribution u(r) in the metal is defined...
  23. C

    Prove Finite Dimensional Normed Vector Space is Differentiable

    Homework Statement Let V be a finite dimensional normed vector space and let U= L(V)*, the set of invertible elements in L(V). Show, f:U-->U defined by f(T)= T-1 is differentiable at each T in U and moreover, Df(T)H = -T-1HT-1 where Df(T)= f'(T). Homework Equations Apparently...
  24. L

    Why take FINITE time for an electron to observe a photon?

    Hi,all Q1: Why take FINITE time for an electron to observe a photon? (Q2: Why not much people answer my questions? Am I put them in a wrong place? what's the definition of General Physics? Classical only?) Thanks in advance? Quuote from Jeff Reid...
  25. A

    Finite Element Analysis of Collision Impact in MD Patran/Nastran

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  26. J

    A small finite universe and some wierd thoughts from it

    I do not have physics education pass A-levels, yet. So what I've been thinking of should be very simple to follow. It's just so fascinating that I'm wondering if any experts could either point a logic flaw, or direct me to material that has already mused over this for me. I understand that...
  27. L

    Why electron absorbs photon costs FINITE time?

    Hi,all, why electron absorb photon costs FINITE time? Not only for electron, when phonon interact with photon(absorbs it) also costs finite time. As I think, it should be instant, can not find any reason for finite time. Helps! Thanks In advance!
  28. S

    Solving Fick's Law by Finite Difference Method

    Hi, i need help in solving a Fick's Law [ (∂c_k)/∂t = D_k (∂^2 c_k)/(∂x^2 ) ] by Finite Difference Method. Previously, I tried solving the Fick's Law by using the Separation of Variable method but that was not the correct way as told by my Prof as the correct way is to use Finite Difference...
  29. P

    Finite Universe: Why Postulate an Infinite Universe?

    If the approximate time since the big band is correct at about 14 billions years, then the universe should have a limit as to how far it has expanded/inflated. Why then do people still postulate an infinite universe ?
  30. S

    Finite non-abelian group of the order pq, pq primes

    Howdy, all. I am not sure if this is the right forum for this question. It isn't exactly an homework question, but it does stem very closely from a homework assignment in a first year graduate course in Abstract Algebra. The assignment has come and gone with limited success on my part, but...
  31. 2

    Infinite of finite life for a shaft

    I am having trouble finding the method to figure out if a shaft has finite or infinite life if it is subjected to a fluctuating load. I know how to solve for n(factor of safety) in these types of problems. Is there a value that if n is above it has infinite life.
  32. Y

    Finite Well and Schrodinger's Equation

    Homework Statement An electron is trapped in a finite well of width 0.5 nm and depth of 50 eV. The wavefunction is symmetric about the center of the well (x = 0.25 nm). If the electron has energy 29.66 eV and ψ(0) = 1.42 (nm)-1/2, then what is the probability for finding the particle in the...
  33. A

    Finite difference method in fortran

    1. I have problem numerical solving of PDE with finite difference method in fortran. it is about optical fibers. At the beginning of the fiber the delta impuls is inserted, and I need function at the end of the fiber. 2. The equation is given in attachement as the code in fortran...
  34. edpell

    Exploring the Finite & Unbounded Universe: The Preferred Frame

    If the universe is finite and unbounded why can not we think of the frame that sits with it's origin at the center of the 4-D sphere as a preferred frame? The preferred frame?
  35. R

    Finite Square Barrier Scattering Example with Reflection Coefficient Calculation

    Hello to all, I am looking at a scattering example in my book. A particle is incident from the left with energy E > Vo. The barrier is of width L, and located between x = 0 and x = L. The solutions to the time-independent Schrodinger equation in eacch of the regions comprising the left...
  36. homology

    Carnot engine with finite reservoirs

    Homework Statement I'm trying to find the final temperature of a carnot engine with two finite thermal reservoirs. We're told that the heat capacities for both reservoirs are constant (and equal) and to regard the change in each reservoir's temperature during any 1 cycle as negligible...
  37. M

    Number of monomials of degree d in finite field F[x]

    Prove that the number of monomials of degree d in finite field F[x] is \binom{n+d}{n} This is not so much a homework question as something I have read and asked my professor about. He said it was too easy and that I should be able to do it and wouldn't help me. I know I'm probably being a...
  38. A

    Finite series within finite series

    Homework Statement I need to find a closed form for what at first light would be a straightforward finite series. Calculating it explicitly to a particular degree is not difficult, but I just can't find the closed form for the general case. Homework Equations For N>m, the series is...
  39. P

    Numerical differentiation using forward, backward and central finite difference

    ive been given this question for a uni assignment: given the function: f (x) = 5(x^1.3) +1.5(7x − 3)+ 3(e^− x) + ln(2.5(x^3)) find the first derivative at all possible points within the interval [0, 6], with step length h = 1 for: forward difference aproximation, backward difference...
  40. M

    Casimir effect and a finite length Tipler cylinder?

    Can the Casimir effect be used to enable a finite length Tipler cylinder to allow for CTCs? Stephen Hawking proved that a functioning Tipler cylinder could not be built unless it either (1) was infinitely long or (2) violated the weak energy condition, meaning that the region can contain no...
  41. quasar987

    Representation of finite group question

    Does anyone know how to prove that any irreducible representation of a finite group G has degree at most |G|? Equivalently, that every representation of degree >|G| is reductible. Thx!
  42. D

    Finite Element Analysis Program

    I am on a research project where I am finding the heat capacitance and thermal conductance of a material and would like to simulate it on a larger scale as material for heated flooring. Is there a program where I can do a looping heating pipe at a set temperature and show the conductance of the...
  43. B

    Finite difference method help (bvp)

    Hi, I'm currently writing a code to solve a steady-state boundary problem across multiple layers of a system. The system involves diffusion-reaction of various species in a porous medium. I am simply using central finite differences to model this setup, which says that essentially -div*J+Q = 0...
  44. C

    Finite Fields and ring homomorphisms HELP

    Homework Statement Assuming the mapping Z --> F defined by n --> n * 1F = 1F + ... + 1F (n times) is a ring homomorphism, show that its kernel is of the form pZ, for some prime number p. Therefore infer that F contains a copy of the finite field Z/pZ. Also prove now that F is a finite...
  45. 3

    The size of the orbits of a finite normal subgroup

    Homework Statement Let H be a finite subgroup of a group G. Verify that the formula (h,h')(x)=hxh'-1 defines an action of H x H on G. Prove that H is a normal subgroup of G if and only if every orbit of this action contains precisely |H| points. The Attempt at a Solution I solved the first...
  46. 3

    Orbits of a normal subgroup of a finite group

    Homework Statement If G is a finite group which acts transitively on X, and if H is a normal subgroup of G, show that the orbits of the induced action of H on X all have the same size. The Attempt at a Solution By the Orbit-Stabilizer theorem the size of the orbit induced by H on X is a...
  47. C

    Is gravitational attraction finite?

    Is there a distance where the curvature in spacetime created by an object's mass ends? Is it a finite gravity well or does the curvature just get infinitely weaker?
  48. Y

    Pauli Exclusion Principle: Finite Creativity or Philosophy?

    Does the 'Pauli exclusion principle' imply that the universe is only finitely creative? It's rather the philosophy than the physics behind it, I'm interested in. I just wanted to be sure I was interpreting this principle correctly. I thought it meant that there are only a discrete amount of...
  49. M

    Finite and infinitesimal Unitary transformations

    Hi I have a question regarding unitary operators: If an infinitesimal operation (such as a rotation) is unitary does this guarantee that a finite transformation will also be unitary? thanks M
  50. T

    Proving a Finite Group is Not Simple

    I found this problem, and I was wondering if I'm on the right approach. Let G be a finite group on a finiste set X with m elelements. Suppose there exist a g\inG and x\inX such that gx not equal to x. Suppose the order of G does not divide m!. Prove that G is not simple. Would it suffice...
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