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. JulienB

    Calculating Planck's integral for finite range of wavelength

    Homework Statement Hi everybody! I am asked to calculate how much of the total radiated power of a light bulb at temperature ##T=2300##K is contained within ##400##nm and ##750##nm. I am also given the average emissivity of tungsten ##\epsilon_\text{ave}=0.288## and the emissivity within the...
  2. Helios

    B Finite Universe vs. Uncertainty Principle

    If I have this right, when we have exact certainty of a particle's momentum, the bounds of this particle's location cannot be determined. Now there are some who believe in a universe of finite volume and so this particle has to be within this volume. So there seems to be a contradiction. Does...
  3. L

    I Finite Square Well: Bond States and Asymmetric Potential Wells

    I am not sure how is it possible that asymetric potential well does not have bond states if ##E<U_1<U_2##. In symmetric case solution always exists. Why this is a case?
  4. A

    Capacitance between point charge and finite plate

    I need help trying to set up this problem. I want to find the capacitance between a point charge and a finite plate (or disk) as the point moves from above the center of the plate to some distance off the plate. I have been able to simulate this problem using FEM, however, there should be a...
  5. Riverbirdy

    Finite difference Method of Wave Equation

    Hi, Physics forum! Just a little push of my doubts I hope somebody could help me with my confusion of one of our home works. I know that all boundary conditions are zero. My doubt is how do I interpret (x,y,0)=0.01 source in the figure? Where is it located in the grid. I am hoping someone...
  6. T

    I Help with infinitesimal transformation to finite transform

    <Moderation note: edited LaTex code> E.g. A rotation by a finite angle θ is constructed as n consecutive rotations by θ/n each and taking the limit n→∞. $$ \begin{pmatrix} x' \\ y' \\ \end{pmatrix} =\lim_{x \to \infty} (I + \frac{\theta}{n} L_z )^n \begin{pmatrix} x...
  7. durant35

    I Can a finite universe end in heat death?

    Hello guys, I was reading some models about the topology and size of the universe (always a controversial topic), then a question came to my mind. It is predicted that our universe will expand until it reaches heat death. Can a closed, finite universe also reach heat death and be described by...
  8. H

    A Hall coefficient's finite temperature experiments in metals

    There are lots of measurements showing strong temperature ($T$) dependence of Hall coefficient ($R_H$) in correlated materials (eg. cuprate superconductors and other oxide materials) and such plots are available in many recent experimental papers. However, I could not find any $R_H$ vs $T$ plot...
  9. M

    Heat Transfer, Finite difference, Curved geometry

    Homework Statement Homework Equations I could really use a push on how to approach this problem. My primary problem is it asks for the heat flux into the page, which makes no sense to me as that is the z direction and this is in the x/y plane. If anyone could explain this problem and maybe...
  10. A

    I Solving Poisson's Equation Using Finite Difference

    I am using the Finite Difference Method to solve Poisson's equation \frac{\partial \phi}{\partial z^2} = \frac{\rho}{\epsilon} To do it is discretized according to the Finite Difference Approximation of the second order derivative yielding the following set of equations for each grid point...
  11. M

    MHB The extension KE/F is finite and separable

    Hey! Let $C$ be an algebraic closure of $F$ and let $f\in F[x]$ be separable. Let $K\leq C$ be the splitting field of $f$ over $F$ and let $E\leq C$ be a finite and separable extension of $F$. I want to show that the extension $KE/F$ is finite and separable. We have that $KE$ is the smallest...
  12. B

    Index of Intersection of Subgroups with Finite Index

    Homework Statement Suppose that ##H## and ##K## are subgroups of finite index in the (possibly infinite) group ##G## with ##|G : H|m## and ##|G:K|=n##. Prove that ##lcm(m,n) \le |G : H \cap K | < mn##. Homework EquationsThe Attempt at a Solution I was able to get the upper bound on ##|G : H...
  13. durant35

    I Finite Universe Models: Exploring Plausible Models

    Hi guys, Based on what I know about the status of modern cosmology the question whether the universe is infinite or finite in extent is still open. Are there any plausible models in which the universe is finite and closed, despite the curvature being close to flat? Thanks in advance.
  14. RJLiberator

    Infimum and Supremum, when they Do not exist in finite sets

    Homework Statement Give an example of each, or state that the request is impossible: 1) A finite set that contains its infimum, but not its supremum. 2) A bounded subset of ℚ that contains its supremum, but not its infimum. Homework EquationsThe Attempt at a Solution I either understand this...
  15. B

    Does a Locally Finite Collection of Subsets Satisfy the Closure Union Property?

    Homework Statement I read somewhere that if ##\{A_i\}## is a collection of subsets in some topological space ##X## that is locally finite, then ##\overline{\bigcup A_i} = \bigcup \overline{A}_i##, but I am having difficulty showing this. Homework EquationsThe Attempt at a Solution I already...
  16. ShayanJ

    A QFT at Finite Density: Refs & Resources for Zero T

    I need to take a look at some references about QFT at finite density but I can't find anything, or at least I don't know where to look. I should emphasize that what I need is QFT at zero temperature and finite density so it seems to me QFT in finite temperature books may not be what I need or...
  17. A

    I Create algebraic function with finite power expansions?

    How would I design a non-trivial algebraic function of degree 4 containing a branch at the origin with the (finite) power expansion: ##w(z)=1+0.5 z-1/4 z^{1/2}+3/4 z^{1/4}##? having the form ## f(z,w)=a_0+a_1 w+a_2 w^2+a_3 w^3+a_4 w^4=0## with the ##a_i ## ( preferably not fractional)...
  18. elixer akm

    B What does it mean when a limit is finite

    What does it mean when a limit is finite
  19. F

    Finite difference method derivation PDE

    Homework Statement Which algebraic expressions must be solved when you use finite difference approximation to solve the following Possion equation inside of the square : $$U_{xx} + U_{yy}=F(x,y)$$[/B] $$0<x<1$$ $$0<y<1$$ Boundary condition $$U(x,y)=G(x,y)$$ Homework Equations Central...
  20. M

    Finding range of bound/non bound state energies of 1D finite

    Homework Statement I'm currently working on a homework set for my intermediate QM class and for some reason I keep drawing a blank as to what to do on the first problem. I'm given three potentials, V(x), the first is of the form {A+Bexp(-Cx^2)}, the others I'll leave out. I'm asked to draw the...
  21. Math Amateur

    MHB Bresar, Lemma 1.3 - Finite Division Algebras .... real quaternions ....

    I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of the proof of Lemma 1.3 ... ... Lemma 1.3 reads as follows...
  22. alexmahone

    MHB Comparing $gH$ and $Hg$ for Infinite & Finite Groups

    Suppose $G$ is an infinite group and $H$ is an infinite subgroup of $G$. Let $g\in G$. Suppose $\forall h\in H\ \exists h'\in H$ such that $gh=h'g$. Can we conclude that $gH=Hg$? What if $G$ and $H$ are of finite orders?
  23. Math Amateur

    MHB Bresar, Lemma 1.2 - Finite Division Algebras ....

    I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of the proof of Lemma 1.2 ... ... Lemma 1.2 reads as follows...
  24. Math Amateur

    I Bresar, Lemma 1.2 - Finite Division Algebras ....

    I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of the proof of Lemma 1.2 ... ... Lemma 1.2 reads as follows: My questions related to the above proof...
  25. Math Amateur

    MHB Another Question Regarding Finite Dimensional Division Algebras - Bresar Lemma 1.1

    I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with another aspect of the proof of Lemma 1.1 ... ... Lemma 1.1 reads as follows: My questions regarding Bresar's proof...
  26. Math Amateur

    I Another Question about Finite Dimensional Division Algebras ....

    I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with another aspect of the proof of Lemma 1.1 ... ... Lemma 1.1 reads as follows: My questions regarding Bresar's proof...
  27. Math Amateur

    MHB Finite Dimensional Division Algebras - Bresar Lemma 1.1

    I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with the an aspect of the proof of Lemma 1.1 ... ... Lemma 1.1 reads as follows: In the above text, at the start of the...
  28. Math Amateur

    I Finite Dimensional Division Algebras - Bresar Lemma 1.1

    I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with the an aspect of the proof of Lemma 1.1 ... ... Lemma 1.1 reads as follows: In the above text, at the start of the...
  29. J

    I Solving the 3D Poisson Equation Using Finite Difference/Volume

    Hi, I'm attempting to solve the 3D poisson equation ∇ ⋅ [ ε(r) ∇u ] = -ρ(r) Using a finite difference scheme. The scheme is simple to implement in 3D when ε(r) is constant, and I have found an algorithm that solves for a non-constant ε(r) in 2D. But I am having trouble finding an algorithm...
  30. TheSodesa

    The width of a finite potential well

    Homework Statement An electron is enclosed in a potential well, whose walls are ##V_0 = 8.0eV## high. If the energy of the ground state is ##E = 0.50eV##, approximate the width of the well. Answer: ##0.72nm## Homework Equations For an electron in a potential well, whose energy is less than...
  31. A

    Magnetic field around a finite wire with different diameter

    In my simulation I have a wire with a fixed current flowing, I observed if I change the diameter of the wire the magnetic field (B) in a fixed point of the space also changes, is it correct?
  32. I

    MHB Prove that Q is not a finite set

    Hello I am trying to prove that $\mathbb{Q}$ is not a finite set. I proceed with path of proof by contradiction. Suppose that $\mathbb{Q}$ is a finite set. Then $\exists\; n \in \mathbb{N}$ such that $I_n \sim \mathbb{Q}$, where \[ I_n = \{i \in \mathbb{Z^{+}} |\; i \leq n\} \] This means that...
  33. A

    I Finite difference method for Schrödinger equation

    Suppose I want to solve the time-independent Schrödinger equation (ħ2/2m ∂2/∂x2 + V)ψ = Eψ using a numerical approach. I then discretize the equation on a lattice of N points such that x=(x1,x2,...,xN) etc. Finally I approximate the second order derivative with the well known central difference...
  34. T

    A Backward finite differences on higher order derivative

    I am trying to solve a system of equations and have a question regarding the validity of my approach when implementing a fifth-order Cash-Karp Runge-Kutta (CKRK) embedded method with the method of lines. To give the questions some context, let me state the problem I am attempting to solve: $$...
  35. M

    B Space Finite? Inconceivable - Thoughts?

    Hi, Is space finite? In my opinion, it is inconceivable that space is finite. If space is finite, what is exactly outside of this stuff we called as space? More space? What exactly surrounds the singularity before the Big Bang event started? If it is nothing that "surrounds" the singularity...
  36. ramzerimar

    I Finite Element Method: Weak form to Algebraic Equations?

    Okay, I'm following a series of video lectures on applications of finite element method to engineering, and the tutor started by demonstrating the mathematical background of FEM using a simple heat transfer problem. He derived the governing equation (in just one dimension): (1)...
  37. T

    Python Using backward vs central finite difference approximation

    I am solving the simple 2nd-order wave equation: $$ \frac {\partial ^2 E}{\partial t^2} = c^2 \frac {\partial ^2 E}{\partial z^2} $$ Over a domain of (in SI units): ## z = [0,L=10]##m, ##t = [0,t_{max} = 10]##s and boundary/initial conditions: $$ E(z=0) = E(z=L) = 0 $$ $$ E(t=0) =...
  38. ShayanJ

    A For finite dimension vector spaces, all norms are equivalent

    I searched for a proof of the statement in the title and found this document. But it just proves that for two norms ## \rho(x) ## and ## ||x|| ##, we have ## m\rho(x)\leq ||x|| \leq M \rho(x) ## for some m and M. But how does it imply that the two norms are equivalent? Thanks
  39. Guaicai

    How to get the results like that in Finite Square Barrier?

    [this thread was moved from the Quantum Physics subforum, hence no template] In this page : http://www.physicspages.com/2012/08/06/finite-square-barrier-scattering/ When the E<V The boundary condition tells us the equation (9) (10) and (11) (12). I tried to get the results from those equation...
  40. A

    I Finite difference Hamiltonian

    Suppose I am given some 1D Hamiltonian: H = ħ2/2m d2/dx2 + V(x) (1) Which I want to solve on the interval [0,L]. I think most of you are familiar with the standard approach of discretizing the interval [0,L] in N pieces and using the finite difference formulas for V and the...
  41. caffeinemachine

    MHB Finite Extension Simple iff Purely Inseparable Closure Simple

    Question. Is it true that a finite extension $K:F$ is simple iff the purely inseprable closure is simple over $F$? I think have an argument to support the above. First we show the following: Lemma. Let $K:F$ be a finite extension and $S$ and $I$ be the separable and purely inseparable...
  42. Guaicai

    Scattering in Finite step potential

    origin page : http://www.physicspages.com/2012/08/08/finite-step-potential-scattering/ No quite understand how the solution come from this equation
  43. L

    I Points of a finite projective line

    I found in Thompson "From Error-Correcting to Sphere Packing and Simple Groups" this on page 131 How do you compute m/n in a finite field? Take the equivalence class 5 given above. Why does 2/5 and 18/22 give 5? thanks
  44. R

    B How can the Universe be infinite and yet have a finite age?

    How can the universe be infinite and yet have a finite age?
  45. Guaicai

    Some questions about the Finite Potential Well

    How the symmetric and antisymmetric have results: A=0,G=H and B=0,G=-H in last picture ?[emoji53]
  46. S

    Finite Element Method: Find Total Mass Matrix of Coupled Element

    Does anyone know how to find the total mass matrix of two coupled element by using Finite Element Method?
  47. T

    I Finite promise games, shock of my life

    I am shocked after reading this: http://googology.wikia.com/wiki/Finite_promise_games So, let's take strong Goodstein function. It is total, but this fact is unprovable in Peano Arithmetics. No problem, I just understand that PA is too weak. Goodstein function is total, just take stronger...
  48. M

    Magnetic Field at any Point Around a Finite Straight Wire

    Hello, First of all, this question does stem from graduate work, but it seems far too simple to tag "advanced". I am looking to write some code to simulate the force from a railgun. The first step in doing this (from a tutorial I found) is to find the magnetic field at any point within the...
  49. G

    A Why does Finite Size Scaling shift the Phase Transition Down?

    See the title. I'm not sure that this is the right place to post this question, but I'm not sure it fits any better on any of the other boards. Let's say you have a phase transition. The correlation length will scale as: ξ = |TC-T|ν This diverges on both sizes of the phase transition. Now...
  50. jdawg

    Using finite difference to solve DE

    Homework Statement d2T/dx2 = 5*(dT/dx) - 0.1*x = 0 T(0) = 50 T(10) = 400 (Δx) = 2I've figured out how to do these problems when Δx = 1, but when it equals any other number it goes wrong. I know you start by plugging in the algebraic approximations for the differential elements, I think maybe my...
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