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. F

    Any compact subset is a contained in finite set + a convex set?

    Homework Statement So I am trying to understand this proof and at one point they state that an arbitrary compact subset of a Banach space, or a completely metrizable space is the subset of a finite set and an arbitrary convex neighborhood of 0. I've been looking around and can't find anything...
  2. F

    Does the compact subset of an infinite Banach have finite span?

    Homework Statement Hi all, I am struggling with getting an intuitive understanding of linear normed spaces, particularly of the infinite variety. In turn, I then am having trouble with compactness. To try and get specific I have two questions. Question 1 In a linear normed vector space, is...
  3. R

    2D FIR Filter & Finite Decomposition

    Hi All, I would like to know how can I call or express the following process! I use a (3x3) 2D FIR Filter for imaging processing with DC = 0, like this: 0 1 1 2 O 2 /8 1 1 0 My filter is such that I can decompose it into finite sates, as my image (medical) can take 9...
  4. R

    Proving Finite Order Elements Form a Subgroup of an Abelian Group

    Homework Statement Prove the collection of all finite order elements in an abelian group, G, is a subgroup of G. The Attempt at a Solution Let H={x\inG : x is finite} with a,b \inH. Then a^{n}=e and b^{m}=e for some n,m. And b^{-1}\inH. (Can I just say this?) Hence...
  5. B

    How Many Bound States Exist in a Half Finite Square Well?

    Homework Statement A particle of mass m is in the potential V(x) = \left\{ \begin{array}{rl} \infty & \text{if } x < 0\\ -32 \hbar / ma^2 & \text{if } 0 \leq x \leq a \\ 0 & \text{if } x > a. \end{array} \right. (a) How many bound states are there? (b) In the highest energy...
  6. A

    Proving Finite Outer Measure Inequality

    Homework Statement Let E have finite outer measure. Show that if E is not measurable, then there is an open set O containing E that has finite measure and for which m*(O~E) > m*(O) - m*(E) Homework Equations The Attempt at a Solution This is what I did... m^*(O) = m^*((O \cap E^c) \cup...
  7. P

    Infinite number of turns in finite time

    Homework Statement A car is moving with a constant speed of 40 km/h along a straight road which heads towards a large vertical wall and makes a sharp 90° turn by side of the wall . A fly flying at a constant speed of 100 km/h , start from the wall towards the car at an instant when the car...
  8. M

    Proof of a set is sigma finite

    Homework Statement if f is integrable, then the set N(f) = {x : f(x)≠ 0} is \sigma-finite Homework Equations i am stucked in this proof , somebody help me pleaseThe Attempt at a Solution if f is simple the it seems the set is finite since otherwise the the integral won't exist but how can it...
  9. L

    Partition a divergent integral into finite values

    Hi there, I am reading an article, but I faced the following problem, and I am wondering if it is well known fact. If the integral of a function on some interval is infinity, can we partition this interval into countable disjoint (in their interiors) subintervals such that the integral...
  10. P

    Finite Difference (Interpolating Polynomial)

    Homework Statement http://puu.sh/1QFsA Homework Equations The Attempt at a Solution I'm actually not sure how to do this question. How do i find Δx^2. I kind of understand the question but I don't know how to prove it. I know that Δy becomes dy when the width becomes...
  11. K

    If the universe is finite in size, what is at the end of it?

    If the universe is finite in size, what is at the very edge of it?
  12. Michael27

    Is the set of prime pairs (p, p+2) finite?

    Hi all, I have been asked the question by a friend of mine who was working on a computer algorithm where he needed pairs of primes to uniquely identify items in a set. What I would like to know is there a way to proof that the set of prime pairs (p, p+2) is finite or infinite. I have been...
  13. marcus

    C* algebras, states, finite graphs

    I recently got (re)interested in C* algebras. Poking around, I gathered that there is some way of constructing a C* algebra corresponding to a finite graph. I'll put some links here in case anyone knows anything about this. At the moment I'm ignorant but hope to find out more. No idea in...
  14. L

    Proving Finite Extension is Algebraic & Example of Converse

    Hi everyone I 'm having difficulty in proving the following theorem theorem: If L/K ( L is a field extension of K) is a finite extension then it is algebraic. Show, by an example, that the converse of this theorem is not true, in general. Can you help me to find an example in this case? Thanks...
  15. E

    Finite Element Methods (global stiffness matrix)

    Homework Statement I have the following practice problem which is presented as follows: What is the size of the global stiffness matrix K (i.e., Kuu) for the 2-D problem? http://imgur.com/KZec3 (Unsolved) http://imgur.com/piv1J (Solved) Homework Equations The Attempt at a...
  16. E

    Example of cover (of a set) having finite sub-covers in collection.

    I think I am not understanding the concept of compactness. Can anyone give me an example of a cover that contains finite sub-covers? for example:- G = {S1,S2, ... }, Sn={(1/n,2/n): n ≥ 2} is an example of cover of set (0,1) but it is an infinite collection.
  17. W

    Finite Difference Method, Leapfrog (2,4) CFL Condition

    Hi. I'm trying to determine the CFL condition for the fourth-order leapfrog scheme. I'm finding 2 as what's published, which does not match what I'm getting. Does anyone know where I can find a von Neumann (or Fourier) stability analysis of the leapfrog (2,4) scheme (so I can compare my work)...
  18. L

    Polynomial finite fields; ElGamal decryption

    Homework Statement Given some ElGamal private key, and an encrypted message, decrypt it. Homework Equations Public key (F_q, g, b) Private key a such that b=g^a Message m encrypted so that r=g^k, t=mb^k Decrypt: tr^-a = m The Attempt at a Solution My problem is finding r^-a...
  19. L

    How Does an Element of a Finite Group Relate to Cryptology Theorems?

    I need help with this theorum, please. How is this (the attachment) true? It's for my cryptology class. The rest of the day's notes are here: http://crypto.linuxism.com/thursday_december_13_2012
  20. T

    How could the set oif natural numbers not be finite

    The set of all possible streams of brain activity arising from all possible configurations of all possible neurons with all possible connections is finite, so if you accept that natural numbers are a creation of the human mind (brain), then don't you have to accept that the set of number is...
  21. T

    How could the set of natural numbers not be finite?

    The set of all possible streams of brain activity arising from all possible configurations of all possible neurons with all possible connections is finite, so if you accept that natural numbers are a creation of the human mind (brain), then don't you have to accept that the set of number is...
  22. G

    Matrix Representation of Operators in a Finite Basis

    Homework Statement I have my quantum mechanics final creeping up on me and I just have a question about something that doesn't appear to be covered in the text. Let's say you have a wave function of the following form for a linear harmonic oscillator: \Psi = c_1 | E_1 \rangle + c_2 | E_2...
  23. A

    Solving by finite difference method

    hi; I have 3 hyperbolic electrodes ,one as a ring and 2 others as endcap electrodes which have potential v and 0 respectively.(quadrupole ion trap) I want to solve potential inside the trap by finite difference method. I don't know how general equations for unshaped materials will change...
  24. E

    Use finite difference method to solve for eigenvalue E

    Use finite difference method to solve for eigenvalue E from the following second order ODE: - y'' + (x2/4) y = E y I discretize the equation so that it becomes yi-1 - [2 + h2(x2i/4)] yi + yi+1 = - E h2 yi where xi = i*h, and h is the distance between any two adjacent mesh points. This...
  25. P

    Electric field from uniform charge of finite length

    Homework Statement A uniform charge Q of length L is placed on the x-axis with one end at the origin as shown a) Find the contribution dE (vector) to the electric field at P on the y-axis a distance y from the origin, from the charge at x in dx, in terms of Q, L, dx, ke, x and y b)...
  26. R

    Proving Existence of g in a Finite Group of Even Order

    Homework Statement Let (G,*) be a finite group of even order. Prove that there exists some g in G such that g≠e and g*g=e. [where e is the identity for (G,*)] Homework Equations Group properties The Attempt at a Solution Let S = G - {e}. Then S is of odd order, and let T={g,g^-1...
  27. E

    MATLAB Use finite difference method to solve for eigenvalue E in Matlab

    Use finite difference method to solve for eigenvalue E from the following second order ODE: - y'' + (x2/4) y = E y I discretize the equation so that it becomes yi-1 - [2 + h2(x2i/4)] yi + yi+1 = - E h2 yi where xi = i*h, and h is the distance between any two adjacent mesh points. This is my...
  28. caffeinemachine

    MHB Finite group of order 4n+2 then elements of odd order form a subgroup.

    Let $G$ be a finite group of order $4n+2$ for some integer $n$. Let $g_1, g_2 \in G$ be such that $o(g_1)\equiv o(g_2) \equiv 1 \, (\mbox{mod} 2)$. Show that $o(g_1g_2)$ is also odd. I found a solution to this recently but I think that solution uses a very indirect approach. Not saying that that...
  29. A

    Gamma Poisson Mixture with finite Gamma

    Dear all I am working with a Gamma-Poisson mixture distribution where (and this is not usual) the support of the Gamma distribution (in fact, I am able to restrict to the neg exponential instead of the Gamma...) is finite, e.g. [0,1]. I would like to derive the mean and a Likelihood...
  30. H

    Infinite and finite countable sets

    Ok I understand the concept of infinite countability and that say the set of all rational #s is infinitely countable, but if I needed to represent the set how do I do that? S={xε rat. # : x= k , k ε a rational #}? that doesn't seem right. Also say I wanted to show a set of finite countable...
  31. S

    How to Modify MATLAB Code for a Beam with Horizontal Distributed Load?

    Homework Statement The problem picture is attached(file 1),its a beam subjected to horizonatal ditributed load 2. Relevant examples the MATLAB solution for rectangular shape with vertical load on the upper right corner is like follow, i try to modify it according to the new picture...
  32. S

    Abstract Algebra: Finite Field

    Show that every finite field with p+1 elements, where p is a prime number, is commutative. I know this has something to do with composite numbers, but I'm not quite sure how to show this.
  33. F

    Interpretation of finite element analysis results

    Hi, Recently started with FEA - loving it, at least the modelling / load application part. Interpreting the results is tricky - particularly around where loads are applied. Got a project (no pics sorry) which has a drilled hole in a plate, and have applied the load as a a pressure...
  34. M

    Finite group with two prime factors

    Homework Statement I am trying to prove the following: Let G be a finite group and let \{p,q\} be the set of primes dividing the order of G. Show that PQ=QP for any P Sylow p-subgroup of G and Q Sylow q-subgroup of G. Deduce that G=PQ. Homework Equations The set PQ=\{xy: x \in P \text{ and }...
  35. aphirst

    1D Finite Planar Photonic Structure - Transfer Matrix Method

    Homework Statement I'm implementing the transfer matrix method (manually) for an EM wave through a 1D layered structure. Basically I'm just considering a plane wave in the positive-x direction, conserving E and H across each material interface, and constructing interface matrices, the...
  36. D

    Why positive curvature implies finite universe?

    This post in influenced by 3 new threads in our cosmology forum. Recent observational data favors positive curvature of our Universe. The question I have, however, is why positive curvature implies spatially finite Universe? Yes, it might look quite obvious if we embed curved space into higher...
  37. G

    Solving Neutron Problems with Commercial Finite Element Method Codes

    As I know, the method to solve neutron problem is divided into two steps now, neutron transport calculation for fuel assemblies and neutron diffusion calculation for whole reactor core, both using specified code such as CASMO and SIMULATE from STUSVIK. I want to know whether the commercial...
  38. B

    Convergence of Finite Sets: A Limit on Repeated Elements?

    Homework Statement Let A be a finite subset of R. For each n in N, let x_n be in A. Show that if the sequence x_n is convergent then it must become a constant sequence after a while. Homework Equations The definition of limit. The Attempt at a Solution As A is finite, at least...
  39. C

    Solving for Eigenvalues in a Finite Square Well with Both Walls Finite

    Homework Statement Already defined that for a 1D well with one finite wall the eigenvalue solutions are given by k cot(kl) = -α Show the eigenvalue solutions to well with both walls finite is given by tan(kl) = 2αk / (k^2 - α^2) Well is width L (goes from 0 to L) with height V_0...
  40. B

    Plane Trusses Finite Elements 2 - Assembled Matrix

    Folks, I am having difficulty understanding how this global matrix is assembled with the naming convention used as shown in attached. The numbers in the corners such as 1(1,2) etc in figure 4.6.3 (b) denote the global and element numbers respectively. Can anyone shed light on how this...
  41. D

    What Factors Affect Neutron Flux in a Finite Medium?

    Deaar all good morning I am very interested to the flux in a slab of extrapolated thickness a, containing distributed sources of neutron. A I have an example in which the source is given as s(x)=S(x+a/2) where S is a constant and x distance from the center of the slab. You mentioned in one...
  42. N

    The universe and its matters: finite or infinite?

    It's been said that the universe has no edge, it's expanding, it has no center and the big bang was the birth of energy, matters and space-time. I also often hear that it's been estimated the universe has approximately 200 billion galaxies or more or much more. Also the number of particles...
  43. C

    Square of a finite deltafunction

    Hi. I'm reading "Quantum Field Theory - Mandl and Shaw" about how to derive the cross-section and in the derivation the authors make the following argument "For large values of T and V, we can then take \delta_{TV}(\sum p_f' - \sum p_i) = (2\pi)^4 \delta^{(4)}(\sum p'_f - \sum p_i) and...
  44. R

    Finite element methods for Yield Line Analysis

    Hi All, I'd like to what kind of steps need to be taken to accurately estimate the yield lines of RC structures. My intention is, to know what type of loading is acting on beams transferred from slabs. I know how to formulate thin/thick plates and shells. The results converges with commercial...
  45. J

    Let G be a finite group. Under what circumstances

    Let G be a finite group. Under what circumstances ... Homework Statement ... is that map δ:G→G defined by δ(x)=x2 an automorphism of F. Homework Equations And automorphism δ:G→G is a bijective homomorphism. The Attempt at a Solution The only circumstance I've so far found is...
  46. B

    Transformation between Global and Local Coordinates for Uniform Bar Elements

    Folks, The element equations for a uniform bar element with constant EA according to the attachment is given as ##\displaystyle \frac{E_a A_e}{h_e}\begin{bmatrix} 1 &0 &-1 &0 \\0 &0 &0 &0 \\-1 &0 &1 &0 \\ 0 &0 &0 &0 \end{bmatrix}\begin{Bmatrix} u^e_1\\v^e_1 \\u^e_2...
  47. C

    Double integrals over finite region

    Homework Statement Evaluate \int_{R} \int \frac{xy^2}{(4x^2 + y^2)^2} dA where R is the finite region enclosed by y = x^2\,\,\text{and}\,\, y = 2x The Attempt at a Solution I think the easiest way to integrate is to first do it wrt x and then wrt y, i.e \int_{0}^{4}...
  48. W

    Question about Finite State Automatons

    I'm reading about automata theory and am currently at the part about what a FSA can recognize and what it cannot. They use the example of some language: {0n1n | n ≥ 0} which an FSA cannot be built for. When I first started learning about state machines before reading into theory of...
  49. X

    Finite Dimensional Vector Space & Span Proof

    Homework Statement So basically, I'm studying the proof for this: "In a finite dimensional vector space, the length of every linearly independent list of vectors is less than or equal to the length of every spanning list of vectors." What the book (Axler's Linear Algebra Done Right 2e) does...
  50. W

    Proof by induction: multiplication of two finite sets.

    Homework Statement prove by induction that if A and B are finite sets, A with n elements and B with m elements, then AxB has mn elements Homework Equations AxB is the Cartesian product. AxB={(a,b) such that a is an element of A and b is an element of B} The Attempt at a Solution...
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