What is Element: Definition and 880 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. L

    A Volume element in Spherical Coordinates

    For me is not to easy to understand volume element ##dV## in different coordinates. In Deckart coordinates ##dV=dxdydz##. In spherical coordinates it is ##dV=r^2drd\theta d\varphi##. If we have sphere ##V=\frac{4}{3}r^3 \pi## why then dV=4\pi r^2dr always?
  2. R

    Show N is a normal subgroup and G/N has finite element

    Clearly e ∈ N. If a, b ∈ N, say ##a^k = b^l = e##, for some k,l ∈ N, then ##(ab)^{kl} = (a^k )^l (b^l )^k = e^l e^k = e##; thus, ab ∈ N. Also, ##|a|=|a^{−1}|##, so ##a^{−1}## ∈ N. Thus, N is a subgroup. As G is abelian, it is normal. Take any c ∈ G. If, for some n ∈ N, we have ##(cN)^n = eN##...
  3. J

    Thevenin isolates nonlinear element

    I have no problem getting the ##R_{TH}## since from the special element's POV, the resistors are in parallel, and that's the answer. However, I don't really understand how to get ##V_{TH}##. Ignoring the special element, it seems that I have the resistors in series this time. But I'm not too...
  4. T

    Abuse of the Finite Element Method

    In general, one could say the Finite Element Method is merely an interpolation method that could be used to solve field equations. Despite that, this question focuses exclusively on the FE Method and its use in Mechanical Engineering. ------------------- I have noticed that some schools now...
  5. rachelmaddiee

    Chemistry Converting the number of atoms to the mass of an element

    Atoms-to-mass conversion Step 1: First, convert the number of atoms to moles, then convert miles to grams Step 2: Second, use the inverse of the Avogadro’s number(moles to number of atoms) Are these the correct steps?
  6. D

    Math/Physics Guidance for Sci-Fi Story Plot Element

    Summary:: 1. At what distance (in km) would a telescope (roughly half the size of Hubble) be able to actually make out features on an approaching object with a 75m cross-section? Hello Everyone, New to the forum, but I've been reading a lot of other posts here and am consistently impressed...
  7. C

    Element of surface area in spherical coordinates

    r,θ,ϕ For integration over the ##x y plane## the area element in polar coordinates is obviously ##r d \phi dr ## I can also easily see ,geometrically, how an area element on a sphere is ##r^2 sin\theta d\phi ## And I can verify these two cases with the Jacobian matrix. So that's where I'm at...
  8. J

    Diffusion equation: time for an element to diffuse at set distance

    Good morning, I'm trying to workout the time for an element to diffuse at set distance in microns. I have the distance, the diffusion coefficient, just unsure which equation I actually use. X= sqrt DT or the other one x= sqrt 2DT. I can't seem to figure out when you use one and not the...
  9. Purahei

    Fortran Discrete Element Method in FORTRAN 90 for collisions of particles

    Does anyone know a simple implementation in FORTRAN 90 of collisions of particles?
  10. D

    I 4-dimensional element volume

    I've come across discussions about the invariant properties of the 4 volume dV=dxdydzdt, but have yet to see its use in many equations. What is this object mostly used in and how is it or would it be used in quantum physics, cosmology, and relativity?
  11. Diracobama2181

    A Volume Element for Isotropic Harmonic oscillator

    I am currently having trouble deriving the volume element for the first octant of an isotropic 3D harmonic oscillator. I know the answer I should get is $$dV=\frac{1}{2}k^{2}dk$$. What I currently have is $$dxdydz=dV$$ and $$k=x+y+z. But from that point on, I'm stuck. Any hints or reference...
  12. P

    MCNP error zero lattice element hit

    I have been encountering "zero lattice element hit" when I try to run it in MCNP5. The input file is provided below. The square lattice runs fine, but the hexagonal does not. Hope someone can help me here. Thank you.
  13. H

    Nonlinear Structural Analysis with Finite Element Method

    Unlike in electromagnetics, the nonlinearity of mechanical structures is not only due to the material property. It could be due to large deformation and contact as well. Even though I will be implementing the existing and popular methods, I am still scared and I feel it is not a job that can be...
  14. T

    B In theory, could any element become unstable?

    Problem Statement: NA Relevant Equations: NA So just smashing through some info on particles and I have come across the term "decay" which seems to be used quite ambiguously. Decay is the process where a nucleus expells radiation as a means to redress the imbalance of forces occurring...
  15. L

    How to find the area element dA in this situation?

    I know how to find the area of a plane which is parallel to the xy-, yz-, or, xz-plane, those are the easiest case. I also tried to find the area of a plane which is only perpendicular to 1 particular axis plane, like the one passing through points (0,0,a), (a,0,a), (0,2a,0), in which case...
  16. K

    Electrical Help with making a heating element with a 3 phase power supply

    hi everyone. my uncle currently has a big "cylindrical rolling cooking pot" (imagine a cement mixer with burners at the bottom) that he uses to cook his stuff, ie sesame seeds. this cooking pot currently runs on gas. as he has been facing some issues with the gas supplier, he intends to...
  17. M

    Effects of Lens Element Aberrations on a Fully Corrected Lens Image

    Leitz Summicron 50 is one of the extremelly well corrected lens in the world. Legend says about this lenses internal elements and their spherical aberrations was responsible of lot of beatiful effects on image. For highly corrected lens image , does high internal aberration really effects the...
  18. T

    What element produces a vapor in comet tails?

    I would like to find out what element produces a vapor or a stream in a heavy charged ionic vacuum would lithium produce such a thing? Comet tails.. just wondering
  19. Shackleford

    PhD in Applied Mathematics - Finite Element Analysis

    My background is BS Math with Physics minor (3.5) and MA Math (3.7) from the University of Houston. My current plan is to explore the necessary background for doing research in finite element analysis. Over the next few semesters, I plan to take Numerical Methods for PDEs, Statistical Computing...
  20. D

    I Can any element be photodisintegrated

    Can any element be photodisintegrated or are there certain elements that can't be photodisintegrated?
  21. SamRoss

    I Is there an algebraic derivation of the area element in polar coordinates?

    There is a simple geometric derivation of the area element ## r dr d\theta## in polar coordinates such as in the following link: http://citadel.sjfc.edu/faculty/kgreen/vector/Block3/jacob/node4.html Is there an algebraic derivation as well beginning with Cartesian coordinates and using ##...
  22. BillTre

    Chemical Element Haikus: Science Magazine Series

    Science magazine, to go with their recent history of the periodic table (I guess), they now have a series of Haiku, one for each element. It is here.
  23. D

    Photovoltaics and time near a black hole (as a key story element)

    I'm a physics student and science fiction writer, and I've never been to this section of PF before! But I have an idea I think is cool for a novel or short story and I'd like some input on the physics involved. As I'm not overly worried about this idea being stolen I'm going to provide a short...
  24. Z

    Simpack force element F042

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  25. K

    What is the area element of angular distribution of charge?

    I'm trying to get the Electric Field of a Thin spherical shell along $$ \hat z $$ axis. In this problem I've got a charge/area density: σ(θ)=σ0⋅cos(θ)σ(θ)=σ0⋅cos(θ). θ∈[0,π]θ∈[0,π] (theta is the polar angle)Can you please help me with how can I know the area element? thanks.
  26. S

    B How does one change the isotope of an element?

    Sorry if this is the wrong subforum i am new here How could one turn Palladium-102 into palladium-103? Would you take a cyclotron and hit it with neutrons? Or would you take Rhodium-103 and hit it with protons? The only reason I ask is because it has a half life of 17 days, and because of that...
  27. Q

    I Deriving the spherical volume element

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  28. A

    Finite Element Model of Euler-Bernoulli Beam Theory

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  29. YoungPhysicist

    Html5 <canvas> element related apps not working

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  30. Alan Lins Alves

    Problem with the Finite Element Method applied to Electrostatics

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  31. F

    Extract anomalies from two-line element set (TLE) on ISS

    Homework Statement I am faced to a problem of interpretation illustrated on figure below : I must precise that I talk about **mean anomaly**. Homework Equations for the 2 questions, I am asked to find : 1) at which anomaly is the ISS at the two lines epoch ? 2) at wchich anomaly is the...
  32. Matthew Strasiotto

    Doping semiconductors compounded from various element groups

    Hi all - This is pulled from a past paper - Homework Statement I'm only going to state the components that I find challenging of this problem - The rest will be attached in my solution set. Essentially - given an intrinsic semiconductor comprised of group II-VI elements. Upon doping with group...
  33. V

    Finding an element using quantum configuration

    havent done this stuff in lile 5-6 years so can't remember half of what to do lel. the first part i would like a yes/no please, Thanks. Given the quantum numbers (6,2,2,+1/2) what is the element, i said UUB becasue the first two numbers indicate 6D and the second would mean its +2 and positive...
  34. Mr Davis 97

    Showing that an element is a unit in a ring

    Homework Statement Let ##S=\{a+bi+cj+dk \mid a,b,c,d \in \mathbb{Z}\}## be the ring of integral Hamiltonian quaternions, where multiplication is defined using the same rules as in ##\mathbb{H}##, the ring of real Hamiltonian quaternions. Define a function $$N:S\to\mathbb{Z}...
  35. M

    Numerics FEA interpolation order vs element number

    Hi PF! Can someone help me understand the difference between interpolation order (linear, quadratic, etc) vs element number? Like, if we had a 1D beam (for simplicity) what's the difference between using 1 element and a quadratic interpolation vs 2 elements but a linear interpolation? Not...
  36. Mr Davis 97

    Show that given conditions, element is in center of group G

    Homework Statement Let ##G## be a finite group and ##m## a positive integer which is relatively prime to ##|G|##. If ##b\in G## and ##a^mb=ba^m## for all ##a\in G##, show that ##b## is in the center of ##G##. Homework EquationsThe Attempt at a Solution Let ##|G| = n## and ##b\in G##. Note that...
  37. S

    MHB Using an MVC to delete an element from an arrayList

    PLEASE HELP! How can I delete a flashcard from my ArrayList? My position never updates and it always deletes position 0. Please let me know if you need more code to examine. I've tried trouble shooting this to find the problem but I can't figure out how to fix it. It's bugging me so badly and I...
  38. L

    Group Theory: Finite Abelian Groups - An element of order

    Homework Statement Decide all abelian groups of order 675. Find an element of order 45 in each one of the groups, if it exists. Homework Equations /propositions/definitions[/B] Fundamental Theorem of Finite Abelian Groups Lagrange's Theorem and its corollaries (not sure if helpful for this...
  39. B

    How can we calculate the power of a heating element?

    To be more specific, if i have to heat water 300l of water in one hour. What should the power of a heating coil?
  40. R

    MATLAB Finite Element Analysis (FEA) in MATLAB - Textbook Guide

    Does anyone know of a great text that shows how to set up FEA in MATLAB in detail. I have wrote out the sort of pre pseudo code from John Andersons - Computational Fluid Dynamics now I just need to build it out in code. I am old school with the hand sketches, hopefully this does not get me a...
  41. Mr Davis 97

    Finding the order of element of symmetric group

    Homework Statement Let ##n## be a natural number and let ##\sigma## be an element of the symmetric group ##S_n##. Show that if ##\sigma## is a product of disjoint cycles of orders ##m_1 , \dots , m_k##, then ##|\sigma|## is the least common multiple of ##m_1 , \dots , m_k##. Homework...
  42. P

    A Is a volume element in relativity represented by a vector?

    Can we say that a volume element can be represented by a vector, or is there some hidden complication that makes this inadvisable? For some background, the stress-energy tensor has been described as the density of energy and momentum, in for instance MTW. So if one says that the represention...
  43. Mr Davis 97

    Order of element and order of cyclic group coincide

    Homework Statement Let ##G## be a group and ##x \in G## any element. Prove that if ##|x| = n##, then ##|x| = |\{x^k : k \in \mathbb{Z} \}|##. Homework EquationsThe Attempt at a Solution Let ##H = \{x^k : k \in \mathbb{Z} \}##. I claim that ##H = \{1,x,x^2, \dots , x^{n-1} \}##. First, we show...
  44. C

    Symmetric bowl associated with a line element

    Hi! I have the following problem I don't really know where to start from: A bowl with axial symmetry is built in flat Euclidean space ##R^3##, and has a radial profile giveb by ##z(r)##, where ##z## is the axis of symmetry and ##r## is the radial distance from the axis. What radial profile...
  45. C

    Null geodesics given line element

    Hi, I'm the given the following line element: ds^2=\Big(1-\frac{2m}{r}\large)d\tau ^2+\Big(1-\frac{2m}{r}\large)^{-1}dr^2+r^2(d\theta ^2+\sin ^2 (\theta)d\phi ^2) And I'm asked to calculate the null geodesics. I know that in order to do that I have to solve the Euler-Lagrange equations. For...
  46. C

    I Christoffel symbols knowing Line Element (check my result)

    Hi! I'm asked to find all the non-zero Christoffel symbols given the following line element: ds^2=2x^2dx^2+y^4dy^2+2xy^2dxdy The result I have obtained is that the only non-zero component of the Christoffel symbols is: \Gamma^x_{xx}=\frac{1}{x} Is this correct? MY PROCEDURE HAS BEEN: the...
  47. enter

    Oddly specific number of elements

    There are 118 elements known to man, and some scientists like Feynman think that element 137 might be the end of the Periodic Table. Isn't that oddly specific? To me, it feels like it is completely random and of no significance. What is going on here? Is there a constant that relates to this...
  48. R

    MATLAB Finite element skeleton code for matlab

    Hello, Does anyone know if a finite element skeleton source code exists. Finite element can be used for structural memebers, gas dynamics, etc. But the over all stepping software is the same and then just input the core equations. My application is for pseudo one dimensional compressible...
  49. Mr Davis 97

    I Showing that every element in G can be written a certain way

    Let G be a finite group which possesses an automorphism ##\sigma## that has no nontrivial fixed points and ##\sigma ^2## is the identity map. Prove that ##G## is abelian. So there's a hint, and it tells me first to established that every element in ##G## can be written as ##x^{-1} \sigma (x)##...
  50. Mr Davis 97

    Showing that an element has order 2 if product of 2-cycles

    Homework Statement Show that an element has order 2 in ##S_n## if and only if its cycle decomposition is a product of commuting 2-cycles. Homework EquationsThe Attempt at a Solution Suppose that ##\sigma \in S_n## and ##| \sigma | =2##. Let the cycle decomposition of ##\sigma## be the...
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