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. walkeraj

    I Praseodymium, other Elements, and their Magnetic Properties vs. radioactivity

    Question: Does the magnetic properties of an element, like Praseodymium, vary with radioactivity? That is, in general, does radioactivity (perhaps beta decay or alpha decay) subtly or otherwise alter the electronic structure enough to alter magnetic properties? The case for beta decay may be...
  2. Eclair_de_XII

    C/C++ Is there a shorter way to determine if a given element is in an array?

    #include <iostream> #include <vector> #include <string> using namespace std; int main(void) { vector <int> v = {0, 5, 9, 3, 2, 1}; bool nine_exists = false; for (int i: v){ if (i == 9) { nine_exists = true; break; } } string message =...
  3. chiyu

    I Vector calculus: line element dr in cylindrical coordinates

    We were taught that in cylindrical coodrinates, the position vector can be expressed as And then we can write the line element by differentiating to get . We can then use this to do a line integral with a vector field along any path. And this seems to be what is done on all questions I've...
  4. Astronuc

    GRX-810, Advanced Multi-principal Element Alloy (MPEA)

    https://www.nasa.gov/image-feature/nasas-new-3d-printed-superalloy-can-take-the-heat I searched for the composition, which I found in an open access Nature article https://www.nature.com/articles/s41586-023-05893-0 Ni bal, 33 Co, 29 Cr, 3 W, 1.5 Re, 0.75 Nb, 0.25 Ti, 0.3 Al, 0.05 C; Nb and Ti...
  5. H

    How to compute the Casimir element of Lie algebra sl(2)?

    Homework Statement: please, could you help me to know hoe I compute the Casimir element of lie algebra sl(2), I know the basis and their relations, but i could not find the book explain in details how we get the Casimir element.. I think it is related to killing form, but also I could not find...
  6. A

    Help debugging MCNP code - particle lost and zero latice element found

    I keep getting particle lost error even though there were no hole in the lattice. Can someone identify any mistake in my code?
  7. chwala

    Problem involving irreducible element -Ring theory

    Hey guys, i need insight on the highlighted part...the steps before this are quite clear: where is the ##\dfrac{3}{4}M ## coming from? and how to show the argument does not work for ##n=-3##? i should be able to check on this ...later. and why is the Norm of say; ##ϒ =a+c\sqrt b## taken...
  8. N

    Length element in Ampere's law

    Why is the length element (vector ds) perpendicular to the current? I though length element should be parallel to current. Would anybody be kind enough to help.
  9. shivajikobardan

    JavaScript How to paint an element in screen using javascript?

    <div class="body"> <div id="board"> <div id="bat" class="bat"></div> <div id="ball" class="ball"></div> </div> </div> This is my HTML. I've done CSS For all of them and generated this: Now, I want the bat to move left and right when I press arrow keys...
  10. M

    A Finite-Discrete Element Method (FDEM) software recommendation

    Hello, I am looking for FDEM software that can do poroelasticity and has a hydraulic solver besides a mechanics solver.
  11. M

    A Rectangular higher order edge element (finite element method)

    I have solved many finite element problems using nodal based (rectangular element) for higher order. now i am trying to solve electromagnetic problem using vector element (Nedelec or Whitney). I know only triangular edge based element with first order only and not higher order. i am searching...
  12. Lluis Olle

    B Metric Line Element Use: Do's & Don'ts for Accelerated Dummies?

    From Wikipedia article about Hyperbolic motion, I have the following coordinate equations of motion for Bob in his accelerated frame: ##t(T)=\frac{c}{g} \cdot \ln{(\sqrt{1+(\frac{g \cdot T}{c})^2}+\frac{g \cdot T}{c})} \quad (1)## ##x(T)=\frac{c^2}{g} \cdot (\sqrt{1+(\frac{g \cdot T}{c})^2}-1)...
  13. A

    B Light element abundances for He3/H?

    I'm trying to understand the Schram plot, which is the graph of wiki here: https://en.wikipedia.org/wiki/Cosmological_lithium_problem I do not understand why the yellow box (the observed light element abundance) for H3/H (red stripe) is absent? Is there any reason for this?
  14. T

    MATLAB FEM, Matlab and the modes of an element

    Hello I wrote a Matlab code to form the 8 by 8 stiffness matrix of a single, 4-noded element, for a plane strain problem for an isotropic element. I conduct an eigenvalue analysis on this matrix Matlabe reports 5 non-zero eigenvalue modes, and 3 zero-eigenvalue modes (as expected) Of the 3...
  15. JH_1870

    A A question about current density in finite element analysis

    I know that if there is only one conductor providing the current density, then the current density can be used. But if you apply Maxwell's equation when there are multiple current sources, I don't know which value to use. This is not an analysis using a tool, but a problem when I develop the...
  16. CPW

    Musing on which element discussed most in physics class

    My child is learning the periodic table for science class, memorizing elements 1 - 20. Middle school. While I assisted, I mused on the elements and on which are discussed most in physics classes. Here is my ranking of the top three: 1. Z=1 2. Z=2 3. Z=92 Do you agree?
  17. Demystifier

    I Geometries from Line Element $$dl^2=d\theta^2 + \sin^2\theta\, d\varphi^2$$

    Consider the line element $$dl^2=d\theta^2 + \sin^2\theta\, d\varphi^2$$ where ##\theta\in [0,\pi]##. The standard interpretation of this line element is to take ##\varphi\in [0,2\pi)##, in which case the line element represents the standard metric of the sphere ##S^2##. However, from the line...
  18. M

    How to apply divergence free (∇.v=0) in nodal finite element method?

    I know how to apply boundary condition like Dirichlet, Neumann and Robin but i have been struggling to apply divergence free condition for Maxwells or Stokes equations in nodal finite element method. to overcome this difficulties a special element was developed called as edge element but i don't...
  19. A

    I Formula for integration of natural coordinates over an element

    In a textbook I own a formula is given for the integration of natural coordinates over an element. In this case it is a 1 dimensional element (i.e. a line segment) with coordinates ##x_i## and ##x_j##. The coordinate ##x## over the element is written as: $$ x = L_1(x) x_i + L_2(x) x_j $$ with...
  20. M

    A When should you use more mesh elements in the finite element method?

    the simple rectangular isoparametric element (curved edges element) can be used to generate many complex shapes like.. square to circle square to triangle two square elements to annular. and the results i calculated in python code (2D case) are very accurate, then i confused why to use complex...
  21. Eclair_de_XII

    B Let f_n denote an element in a sequence of functions that converges

    Let ##\epsilon>0##. Choose ##N\in\mathbb{N}## s.t. for each integer ##n## s.t. ##n\geq N##, $$|\sup\{|f-f_n|(x):x\in D\}|<\frac{\epsilon}{3}$$ where ##D## denotes the intersection of the domains of ##f## and ##f_n##. Choose a partition ##P:=\{x_0,\ldots,x_m\}## with ##x_i<x_{i+1}## where...
  22. S

    [BASIC language] Removing an array element -- how?

    I cannot figure how to do this. I looked through some old programming textbook and tried an online search and still cannot find. How can one element from an array be removed, and then the array put together but now with the one item less, and so the array is now one item smaller than it was...
  23. Eclair_de_XII

    Fortran How do I create a pointer to an element of an array with a variable index?

    program main implicit none real,dimension(3),target::x=[0,4,5] real,pointer::y call point_to_biggest(x,y) !print *,y ! For testing purposes; to be unmuted only when y points to something contains subroutine point_to_biggest(array,ptr) implicit none...
  24. Salmone

    I Matrix element in problem with hydrogen atom

    I have a problem in calculate a matrix element in a problem with hydrogen atom. I have an hydrogen atom and Hamiltonian eigenstates ##|n,l,m>## where ##n## are energy quantum numbers, ##l## are ##L^2## quantum numbers and ##m## are ##L_z## quantum numbers, I have to calculate the matrix element...
  25. T

    The 8 Mode Shapes of a plane finite element

    I recall, about 30 years ago, seeing the eight mode shapes (and eigenvalues) of a single plane stress (or strain) finite element. Also, years ago, I wrote a FORTRAN code to obtain them (using IMSL libraries) I know there are eight (because the plane quad element had 8 degrees of freedom) I...
  26. F

    What's the best shape function/element in finite element methods for phase field simulation?

    What's the best shape function/element in finite element methods for phase field simulation?
  27. BenDover

    Oxygen gas produced by a Solid element + sodium hydroxide solution?

    Hello. I am wondering; which solid at room temperature elements produce oxygen gas when put into a solution of sodium hydroxide? Thanks
  28. docnet

    Show that gcd(a,b) is the smallest positive element in the set {ma+nb}

    ##m##, ##n##, ##a##, and ##b## are in ##\mathbb{Z}##. The set of natural numbers is an abelian group, so ##\{ma+nb|m,n\in\mathbb{Z}\}## is a subset of ##\mathbb{Z}##. ##a ## and ##b## are either relatively prime or not relatively prime. If ##a ## and ##b## are relatively prime, then there are...
  29. D

    How replace a numeral in the string 'abc1def' w/ an array element?

    Summary:: I need to loop through a number of strings replacing the numerals in them with an array element so that e.g.: flos1Field, flos2Field, flos3Field, etc. become flosAField, flosBField, flosCField. The array would be something like: const letters = ["A", "B", "C"]; I put the question in...
  30. U

    COMSOL: stress on a sensor, how to use infinite element domain?

    At the risk of waiting hours on simulations of a sensor, I was wondering if I could use infinite element domain on COMSOL to simplify it. The first image consists of what I would like to simulate but found out that the simulation time is a huge factor as I have a lot to simulations to conduct...
  31. Purpleshinyrock

    Does element x present a linear resistance?

    ANSWER: element x does not present a linear resistance because it isn't constant as i and v increases. Is my answer correct?
  32. KyleGranger

    Best high performance computer build for finite element simulations

    I want to build a high performance computer optimized for FEA. If anyone has any suggestions or experience with this, please chime in. I'm looking for suggestions on processors, RAM, video card, ALL of it!
  33. M

    Comsol: Infinite Element Domain module

    Hello folks, I want to simulate a 2D heat transfer process in the subsurface on a region which is infinite on the r-direction. So, as you know, the very basic way to model this is to draw a geometry that is very long in the r direction. I have done this, and the results that I obtain is correct...
  34. muissi97

    Chemistry Emission Spectrum of an element

    The difference in energy between these two lines is that in the ultraviolet spectrum line, there is more energy because it has a shorter wavelength compared to the visible spectrum line as shown in figure 1.1 According to the Niels Bohr's model of the atom(figure 1.7) and figure 1.1, the least...
  35. F

    Existing work on finite element result analysis

    Is there any existing work focusing on analyzing finite element visualized results and how they differ from analytical solutions, rather than on the method?
  36. C

    Maple Boundary finite element method in Maple

    I would like any tips about a Maple ''home made'' program that I received for a project but this program seems to stop before the very end of the code. I want to find de lift of an airfoil with Boundary finites elements method. I have this error at the very end : Error, (in fprintf) number...
  37. P

    The resistance of an element shaped like a half-cylinder

    So I started doing this with formula: S is equal to π/2*(r2^2-r1^2) l is equal to h Is it correct ?
  38. Bishal Banjara

    I Inverting the metric coefficients in the Schwarzschild line element

    Assuming the line element ##ds^s=e^{2\alpha}dt^2-e^{2\beta}dr^2-r^2{d\Omega}^2 ##as usual into the form ##ds^s=e^{-2\alpha}dt^2-e^{-2\beta}dr^2-r^2{d\Omega}^2##, I found that the ##G_{tt}## tensor component of first expression do not reconcile with the second one though, it fits for ##G_{rr}...
  39. steve1763

    A Find 2D Geometry of Line Element in Coordinates

    i'm trying to find what sort of 2-d geometry this system is in, I've been given the line element 𝑑𝑠2=−sin𝜃cos𝜃sin𝜙cos𝜙[𝑑𝜃2+𝑑𝜙2]+(sin2𝜃sin2𝜙+cos2𝜃cos2𝜙)𝑑𝜃𝑑𝜙 where 0≤𝜙<2𝜋 and 0≤𝜃<𝜋/2 Im just not sure where to start. I've tried converting the coordinates to cartesian to see if it yields a...
  40. L

    A Order of group, Order of element

    If group ##(G,\cdot)## is defined with two generators ##a## and ##b##. And ##a^n=e##, ##b^{m}=e##. Is there any Theorem to tell us what is the largest group they can form?
  41. steve1763

    A Determining Geometry of Line Element: A General Method?

    Is there a general method to determine what geometry some line element is describing? I realize that you can tell whether a space is flat or not (by diagonalising the matrix, rescaling etc), but given some arbitrary line element, how does one determine the shape of the space? Thanks
  42. I

    Comp Sci Searching Array for an Element using Linear Search

    I write a Linear Search code,then ı decided ask to user "r" and "int arr".I mean,User decide their r and arr numbers.I tried scanf("%d",r); command but doesn't work This code my first code before the decide Ask user : #include <stdio.h> int search(int arr[], int n, int r) { int i; for...
  43. Saptarshi Sarkar

    Grating element of an acoustic grating

    I was reading a pdf on acoustic grating for my practicals when I saw that the grating element of an acoustic grating is equal to the wavelength of the sound wave. I also checked a few other sources and got the same. I do not understand why. I know that for an acoustic wave, the standing wave...
  44. Elias_HH

    Engineering How to draw a block diagram of a discrete element with its impulse response

    Hello friends, I have a problem with a exercise sheet. Given is the impulse response of a discret element. The task is to draw the block diagram. But I think that the solution in the sheet is wrong. Because based on the difference equation (Exercise.pdf) there should be 3 delay elements. I have...
  45. burian

    Trajectory of a mass element in a string overhanging a pulley

    Hello everyone, this is a thought experiment I made, it involves two ropes being pulled of a pulley similar to an atwood machine, and a block attached to the two pulleys at the other end. The ropes are being pulled at a constant velocity $ U$ from the end away from the block and the block rises...
  46. Kiah Palmer

    Chemistry Mass of an element required for a chemical reaction equation

    Conversion: 9.65 kg = 9650 g Mass Al = 26.98 g/mol Molar Mass Al2O3 = (2 x 26.98) + ( 3 x 16.00) = 101.96 g/mol Mol Al2O3 = 9650 g / 101.96 g/mol = 94.65 mol Mol Al Required = 94.65 mol x 2 = 189.3 mol Mass 100% Al required = 189.3 mol x 26.98 g/mol = 5.107x103 g Mass 80% Al required =...
  47. R

    Mass spectrometer with a Lead element

    Summary:: How to load the plates with the Lead element in the spectrometer I have a mass spectrometer with lead element which has an electronic configuration 1s^2 2s^2 2p^6 3s^2 3p^6 3d^10 4s^2 4p^6 4d^10 5s^2 5p^6 4f^14 5d^10 6s^2 6p^2. It has 2 free electron, so the ejected electrons go...
  48. J

    Chemistry Find the mass of one element of a sample

    1 mole of K2CrO4 has formula mass of ((2 x K) + (1 x Cr) + (4 x O)) g => ((2 x 39.0983) + (1 x 51.9961) + (4 x 15.9994)) g = 194.1903 g we have 2 moles of K in 1 mole of K2CrO4 = (2x 39.0983) g = 78.1966 g so for 1 mole of substance we have 78.1966 g So how many moles of the substance do we...
  49. P

    Engineering Finite Element Analysis / Structural Analysis

    Hello engineer's community ! I got a problem. If i got a truss frame with 2 bars and an initial nodal displacement for the common node , then how can i calculate the velocity of the oscillation as function of time ? (the 2 bars have different length , same elasticity modulus , same density and...