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. J

    Find all the permutations given some finite characters

    Well I am coming across problems like finding permutation of some n characters. On paper I can find all the permutations given some finite characters easily but when it comes to programming it is hard, why? Why is it hard to tell a computer what I myself can do it so easily? This is strange -...
  2. I

    Standard Finite Well Problem (Solve without symmetry)

    Homework Statement Solve the energy eigenvalue problem for the finite square well without using the symmetry assumption and show that the energy eigenstates must be either even or odd. Homework Equations The finite well goes-a to a and has a potential V0 outside the box and a potential...
  3. AGNuke

    Field inside a finite solenoid - At the ends and in the middle

    A solenoid of length 0.4 m and diameter 0.6 m consists of a single layer of 1000 turns of fine wire carrying a current of 5 x 10-3 A. Calculate the magnetic field strength on the axis at the middle and at the ends of the solenoid. I know the field inside a long solenoid, B = μNI, which is...
  4. B

    Introduction to Finite Element Analysis

    Folks, I have the book An Introduction to the Finite Element Method by J.N Reddy. The following website provides http://highered.mcgraw-hill.com/sites/0072466855/student_view0/executables.html access to the Fortran Executable but I am not sure how to work them. I am just beginning to...
  5. I

    Prove that a nonempty finite contains its Supremum

    Prove that a nonempty finite S\,\subseteq\,\mathbb{R} contains its Supremum. If S is a finite subset of ℝ less than or equal to ℝ, then ∃ a value "t" belonging to S such that t ≥ s where s ∈ S. This is the only way I see to prove it, I hope your help :)) Regards
  6. R

    Abstract algebra, finite A-module

    Homework Statement Let A be an integral domain with field of fractions K, and suppose that f\in A is non zero and not a unit. Prove that A[\frac{1}{f}] is not a finite A-module. [Hint: if it has a finite set of generators then prove that 1,f^{-1},f^{-2},...,f^{-k} is a set of generators for...
  7. J

    Can there ever be a finite pattern?

    A pattern that does not continually re-occur?
  8. H

    Finite amount of degree of freedom for entropy available in universe (?)

    The spectrum of the Cosmic Microwave Background radiation - the flash of the Big Bang, aligns almost precisely with the shape of the Black Body radiation curve. This means that the CMB radiation came from a state that was in thermal equilibrium. Since thermal equilibrium is a state of maximum...
  9. C

    Energy/Mass transitioning from finite to infinite amounts

    E=MC2, if I understand it correctly, tells us that an object would need an infinite amount of energy and mass in order to travel at light speed, which is why particle accelerators can only travel at 99.99999 or so percent of the speed of light. With this in mind I have a couple of questions...
  10. H

    Prove every Hausdorff topology on a finite set is discret.

    Homework Statement Prove that every Hausdorff topology on a finite set is discrete. I'm trying to understand a proof of this, but it's throwing me off--here's why: Homework Equations To be Hausdorff means for any two distinct points, there exists disjoint neighborhoods for those points...
  11. T

    Finite and infinite group

    what is an infinite group that has exactly two elements with order 4? i let G be an infinite group for all R_5 ( multiplication modulo 5) within this interval [1,7) so i got |2|=|3|=4. i'm not sure this is the right answer but i couldn't think of anything else at a moment. help please.
  12. B

    Finite Element Analysis - Author J.N Reddy Book

    Folks, Is there anyone out there familiar with 'An introduction to the Finite Element Method' by J.N. Reddy? I am struggling to decipher what is happening on page 129 as shown in the attachment. If some-one is willing to help I will reply with a more specific query on that page. Thanks
  13. V

    Finite difference approximation question

    Hi, I have a question regarding finite difference approximation: Consider the finite difference approximation u'(xj-1/2) + λu(xj−1/2) ≈ 1/h*[u(xj ) − u(xj−1)] + λ(θu(xj ) + (1 − θ)u(xj−1)) how can I Find the order of approximation as a function of θ? I am really new in this field, so...
  14. S

    How to find gradient of a variable in 3D mapped finite element domain

    Hello, I know the value of a field variable in a 3d mapped finite element mesh. Can anyone suggest an effective method/methods to find its gradient throughout the mesh.
  15. L

    Finite Limit Problem: Understanding cosx/x^0 = 1

    Homework Statement I've read in my textbook, and confirmed via WolframAlpha that lim x->0 (cosx/x^0) =1 , and need an explanation for it. I thought it should be ∞ or something undefined, since 0^0 is undefined. Homework Equations The Attempt at a Solution I tried to use L'Hospitale on the...
  16. B

    Simplifying finite geometric series expression

    Homework Statement I've come across the type of sum in several places/problems but seem to be making no progress in trying to simplifying it further. We have a finite series of some exponential function. \sum_{n=0}^{N}e^{-na} Where a is some constant, a quantum of energy or a...
  17. B

    Engineering Sequence detector, finite state machine circuit

    Homework Statement Please see the attached photo. (The one with the green highlighter), I haven't written it out to avoid mistakes. Homework Equations None. The Attempt at a Solution I have constructed a moore state diagram, a state transition table and come up with boolean...
  18. L

    The Role of Boundary Conditions in the 2D Ising Model: A Finite Lattice Study

    http://books.google.rs/books?id=vrcHC9XoHbsC&pg=PA252&lpg=PA252&dq=Nolting+Finite+Ising+lattice&source=bl&ots=5uRHp0iALf&sig=_YBUSvbCBbhNQJ5Zu1go9AsEkM8&hl=sr&sa=X&ei=y_E4UIEyyobiBPvFgMgM&ved=0CC0Q6AEwAA#v=onepage&q=Nolting%20Finite%20Ising%20lattice&f=false A finite lattice X with so...
  19. S

    Any useful analog to finite differences for matrix products?

    Various closed form formulas for summing the first n terms of a sequence \{a_i\} of numbers can be developed by considering the various order differences of the terms, such as {\triangle} a_i = a_{i+1} - a_i and \triangle^2 a_i = \triangle ( \triangle a_i) . Closed form formulas occur if...
  20. M

    How does the author determine the elements of order p or 4 in the group?

    My question is about the shaded area in the attachment? How did the author get that all the elements of order p or 4 of L are contained in K? I mentioned the abstract but I do not think there is a need for that. Help?
  21. S

    Expectation value of a finite well, and superposition of first two states.

    Homework Statement the first two energy eigenstates of a 1 nm wide finite well of barrier height 8vo have energy eigen values of 0.66ε and 2.6ε. calculate the expectation value of a linear superposition of these states? Homework Equations airy equations The Attempt at a Solution...
  22. beyondlight

    DFT of a finite lengt sequence

    Homework Statement Consider the finite length x[n]= 2δ[n]+δ[n-1]+δ[n-3] We perform the following operation on this sequence: (i) We compute the 5-point DFT X[k] (ii) We compute a 5-point inverse DFT of Y[k]=X[k]2 a) Determine the sequence y[n] for n= 0, 1, 2, 3, 4 b) If N-point...
  23. S

    Prove that the proper subset E of a finite set F can never be equivalent to F.

    Homework Statement Statement: A set F can never be equivalent to its proper subset E This statement appears in Halmos's Naive set theory in the chapter 13. Arithmatic. He arrives at this statement through the following steps 0. In the previous chapter, he proves the recusrsion theorem...
  24. A

    Solving one dimension steady state heat equation with finite differences

    I have a project where I need to solve T''(x) = bT^4 ; 0<=x<=1 T(0) = 1 T'(1) = 0 using finite differences to generate a system of equations in Matlab and solve the system to find the solution So far I have: (using centred 2nd degree finite difference) T''(x) = (T(x+h) - 2T(x) +...
  25. G

    Solving IVP w/ Finite Difference: Strange Oscillations

    Hallo, I tried to use 'finite difference' method to solve a Initial Value Problem(IVP). For the two boundaries I used periodical condtion and for the differential operators I used 4th degree center approximations. But as result, I got this thing. Where comes this strange oscillation What do you...
  26. D

    What are the applications of permutations of a finite set?

    I am having trouble understanding the permutations of a finite set in general. I want to know what it may be used for, and how to solve some of its problems (examples?). In my attachment, I post some pictures of what I am currently reading, and what has confused me.
  27. G

    Total energy vs. energy in a finite region

    I was thinking about the following thing: we know that if the Lagrangian in field theory doesn't depend on the spacetime position, the Noether's theorem says that the stress-energy tensor is conserved, and that T^00 is the energy density at spacetime point x. Then if one integrates this h(x)...
  28. L

    Calculating a Finite Series: Finding Symmetry and Inductive Formulas

    Hello, I would love some help on calculating the following sum for \alpha, \beta \in \mathbb{N} and n \in \mathbb{N} \backslash \{0\}: \displaystyle\sum_{i=1}^{n-1}i^{\alpha}(n-i)^{\beta}. Thanks in advance, Latrace
  29. P

    Surface flux through a single finite element

    Hi, I'm facing a real-life problem and I don't what specific mathematics topic it's related to. Homework Statement I know the value of the components of a vector field in three points of space and I have to find the flux of this vector field through the surface defined by those...
  30. T

    Find a direct summand of a finite abelian group

    Homework Statement If G is a finite abelian group, and x is an element of maximal order, then <x> is a direct summand of G. Homework Equations The Attempt at a Solution I claim that the hypothesis implies that A = G\<x> \bigcup {e} is a subgroup of G. If so, then since G = < <x> \bigcup A>...
  31. H

    Can a finite series like this be evaluated?

    I came across this series by recognizing a pattern while trying to evaluate an integral. I was wondering if the series could be solved in a generalized form where n can vary, and if so, can the limit then be taken as n approaches infinity? You can't take the infinite series without first...
  32. A

    Finite Difference Method - clarification of a term

    Homework Statement I'm doing a class on Numerical Solutions of DE and I have my first assignment. The problem is stated: Consider the following second order boundary value problem: \epsilon \frac{d^{2}y}{dx^{2}} + \frac{1}{2+x-x^{2}} \frac{dy}{dx}-\frac{2}{1+x}y = 4sin(3x), y(0) = 2, y(2) =...
  33. T

    Showing a finite field has an extension of degree n

    Homework Statement Suppose F is a finite field and n > 0. Show that F has a field extension of degree n Homework Equations Tower Law. The Attempt at a Solution Let p^m be the size of F It's trivial to note by characterization that there exists a finite field G' of size...
  34. B

    MHB Sum of a discrete finite sequence

    Hii everyone, I have a sequence {ai,1<= i <=k} where i know the sum of this sequence(say x). I want to know the sum of another sequence {bi, 1<=i <=k}(at least a tight upper bound) where bi=ai*(1/2^i). Or in other words, if you know the sum of the ratio sequence and sum of 1 sequence, how to...
  35. J

    Proof of Cauchy's Theorem for Finite Groups

    I know that this is a lot, but I would love some help. My trouble is at the end of Part II. Theorem (Cauchy’s Theorem): Let G be a finite group, and let p be a prime divisor of the order of G, then G has element of order p. Proof: Suppose G is a finite group. Let the order of G be k. Let p...
  36. J

    Finite Order of Elements in Groups with Normal Subgroups

    Proposition: If every element of G/H has finite order, and every element of H has finite order, then every element of G has finite order. Proof: Let G be a group with normal subgroup H. Suppose that every element of G/H has finite order and that every element of H has finite order. We wish to...
  37. R

    Finite axiomatizability of a Theory

    Hello to everyone, I would like to ask what does it mean that a theory is NOT finitely axiomatizable? What are the pleasant and unpleasant consequences of that?
  38. D

    Does A Finite Integral Over The Plane Imply A Function Is Bounded?

    Suppose I have a C∞ function, which I wish to prove attains its maximum/minimum. First I must prove that the function is bounded at all. If I determine R, the region (of the plane in this case) where the function is strictly positive, and integrate over R to find a finite answer, can I say the...
  39. D

    Finite element simulation of a solenoid

    Hi all. I would like to do a finite element simulation of a coil in a time-varying magnetic field, to see how much current is induced in the coil, and also to see how the coil itself affects its surroundings. Now my question is, how do I model a coil with several thousand turns in a practical...
  40. L

    What is the sum of a finite series with a constant p and variable n?

    Just wondering, is there a way to sort of "collapse" a finite series (to get the sum) that isn't classified as arithmetic, geometric or a p-series.
  41. M

    Infinte distance with finite energy?

    Let's say we have an object. And we then say that E = (1/2)mv2. so we solve for velocity and say that v = (2E/m)^(1/2) then integrate both sides with respect to time ∫(2E/m)^(1/2)dt= ∫v dt so we then have (2E/m)^(1/2)t = distance so if time was infinitely large (long) could an...
  42. N

    [group theory] Finite presentations and relations <S|R>

    Homework Statement Let G be a finitely presented group. Suppose we have a finite generating set S. Prove that there is a finite set of relations R \subset F_S such that <S|R> is a presentation of G. Homework Equations NA The Attempt at a Solution I don't know how to do this. I think...
  43. R

    Probability of finding particle in 1D finite potential well

    Homework Statement ψx is the function of postion for a particle inside a 1D finite square well. Write down the expression for finding the particle a≤x≤b. Do not assume that ψx is normalised. Homework Equations The Attempt at a Solution This is to check I'm not going insane: P...
  44. Z

    Magnetic vector potential of finite wire

    Homework Statement The problem statement is attached. The Attempt at a Solution I know how to solve the problem. However, my teachers solutions notes and my book's do it differently, and I want to ask what the difference is, so I have attached them both. My book does it the way I did it. My...
  45. C

    Is H a Free Commutative Group of Rank n in Z^n?

    show that H is subgroup of finite index in Z^n exactly when H is free comutative group of rank n
  46. C

    Prove: sum of a finite dim. subspace with a subspace is closed

    Homework Statement Prove: If ##X## is a (possibly infinite dimensional) locally convex space, ##L \leq X##, ##dimL < \infty ##, and ##M \leq X ## then ##L + M## is closed. Homework Equations The Attempt at a Solution ##dimL < \infty \implies L## is closed in ##X## ##L+M = \{ x+y : x\in L, y...
  47. F

    Regarding fixed points in finite groups of isometries

    There is a theorem for finite groups of isometries in a plane which says that there is a point in the plane fixed by every element in the group (theorem 6.4.7 in Algebra - M Artin). While the proof itself is fairly simple to understand, there is an unstated belief that this is the only point...
  48. E

    Finite Definition of Languages problem

    Homework Statement A palindrome over an alphabet Ʃ is a string in Ʃ* that is spelled the same forward and backward. The set of palindromes over Ʃ can be defined recursively as follows: i) Basis: λ and a, for all a that are elements of Ʃ, are palindromes. ii) Recursive step: If w is a...
  49. D

    How many bounces does it take for a ball to travel 1854.94320091 feet?

    Homework Statement A ball is dropped from a 100 feet and has a 90% bounce recovery. How many bounces does it take for the ball to travel 1854.94320091 feet? Homework Equations -None- The Attempt at a Solution I know the ratio is .9 and the 'a one' value is 180, so I plugged those values in...
  50. S

    A compact, bounded, closed-range operator on a Hilbert space has finite rank

    Homework Statement Let H be an \infty-dimensional Hilbert space and T:H\to{H} be an operator. Show that if T is compact, bounded and has closed range, then T has finite rank. Do not use the open-mapping theorem. Let B(H) denote the space of all bounded operators mapping H\to{H}, K(H) denote...
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