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).

View More On Wikipedia.org
Recent contents Top users
  1. Mr Davis 97

    I Given order for every element in a symmetric group

    Compute the order of each of the elements in the symmetric group ##S_4##. Is the best way to do this just to write out each element's cycle decomposition, or is there a more efficient way?
  2. beefbrisket

    I Meaning of cross terms in line element

    In a problem from Hartle's Gravity, we are asked to express the line element in non-Cartesian coordinates u, v which are defined with respect to x, y. I have no problem getting the new expression for the line element, but then we are asked if the new coordinate curves intersect at right angles...
  3. karush

    MHB Find order of each element,

    $\text{1. Find order of each element, find the generator ($\delta$) of any properties}$ $$\displaystyle Z_q^*=\left\{ 1,2,4,5,7,8\right\}$$ 2. Viergrappen:group of the table a. leave true $\pi_0$ b. $\pi_x$ rotation about x-axis c. $\pi_y$ rotation operations 'compostion' d. $\pi_y$...
  4. Arman777

    Python Removing a list element that repeats itself -- Solved

    I have an array that looks like A=[0,0,1,1,2,5,6,3,7,7,0,0,1,1,2,5,6,3,7,7] since the "0,0,1,1,2,5,6,3,7,7" part reapeats itself I don't need the second part so for a given array it should give me A=[0,0,1,1,2,5,6,3,7,7] I can't use the set() function and I don't know what else I...
  5. N

    How to control the weight of an object?

    Hello everyone, First off, i would like to apologize for any spelling errors. I am Portuguese and my english is going to be very simple. I am in the process of building something and i am reaching out to the physics community for help solving a problem. I am a CNC programmer and while i was in...
  6. Destroxia

    Calculating Christoffel Symbols from a given line element

    Homework Statement Given some 2D line element, ## ds^2 = -dt^2 +x^2 dx^2 ##, find the Christoffel Symbols, ## \Gamma_{\beta \gamma}^{\alpha} ##. Homework Equations ## \Gamma_{\beta \gamma}^{\alpha} = \frac {1}{2} g^{\delta \alpha} (\frac{\partial g_{\alpha \beta}}{\partial x^\gamma} +...
  7. R

    Mohr's circle with weld across element

    Homework Statement [/B] problem - https://imgur.com/SKeTUXNHomework Equations Mohrs circle The Attempt at a Solution [/B] I have drawn 2 induced loading elements (shown at the bottom of of my working) I just seem to have conflicting information from some class examples and am wondering...
  8. phyzguy

    A Neutron star collisions as a heavy element source

    There was a lot of discussion after the recent observation of the merger of two neutron stars about whether or not these events are the source of the heavier elements. See this thread, for example. This recent paper has some new analysis. Especially interesting is Figure 10, that I've...
  9. Sayak Das

    Finding the inverse metric tensor from a given line element

    Defining dS2 as gijdxidxj and given dS2 = (dx1)2 + (dx2)2 + 4(dx1)(dx2). Find gijNow here is my take on the solution: Since the cross terms are present in the line element equation, we can say that it's a non-orthogonal system. So what I did was express the metric tensor in form of a 2x2...
  10. V

    I I am interested in Schrodinger equation with tempor. element

    I am interested in Schrodinger equation with the temporal element and the calculation of the probability when its depend on 3 variable coordinate and time? How to calculate it and norm it? Probability = (integral x,y,z...0 to infinity) * (integral t...0 to infinity)=1 ?
  11. C

    Is it possible to make a passive element that doesn't reemit EM

    Is it possible (and if so how practical) to overdamp a conductor wire that is many times longer than the wavelength of the incident radiation so that it doesn't reradiate any detectable amount, turning practically all incident radiation into heat?
  12. J

    Reactive power requirement requires which element

    Homework Statement Homework Equations I think it should be A for 1st and B for 2nd Shunt capacitor is used to improve power factor by giving reactive power to line. Series capacitor is used to improve efficiency of line as it nullifies effect of line inductance. And for 2nd Q proportional to...
  13. Z

    Big Omg(f1) subs of Big Omg(f2) iff f1 element BigOmg(f2)

    Homework Statement I usually struggle with proofs and would appreciate some help with the following problem: Prove the following fact: \Omega(f_1) \subseteq \Omega(f_2) iff f_1 \in \Omega(f_2) Homework Equations \Omega(f_1) is the set of functions g s.t. g(n) \geq c f_1(n) where...
  14. C

    Finite element solving of Laplace's equation doesn't converge

    Homework Statement I'm trying to solve Laplace's equation numerically in 3d for a charged sphere in a big box. I'm using Comsol, which solves using the finite elements method. I used neumann BC on the surface of the sphere, and flux=0 BC on the box in which I have the sphere. The result does...
  15. M

    Is there a material or an element that can repel hydrogen?

    I’m working on an idea that I have, and I was wondering if there was something that could repel hydrogen. Not water, not oxygen, just hydrogen. Thanks!
  16. gasar8

    How Does Deformation Affect Surface and Volume Elements on a Sphere?

    Homework Statement Show that the surface and volume element on a deformed sphere are \sigma = \frac{\rho^2 \sin \theta}{\cos \gamma} d\phi d\theta, dV = \rho^3 \sin \theta d\phi d\theta, if \gamma is the angle between normal vector and radius vector. Homework Equations n\cdot r = \cos...
  17. Deepak dabby

    How can I cool down and heat up any liquid with the same element.

    Hlo
  18. A

    Understanding the Dicyclic Group of Order 12: Composition and Element Orders

    Homework Statement The dicyclic group of order 12 is generated by 2 generators x and y such that: ##y^2 = x^3, x^6 = e, y^{-1}xy =x^{-1} ## where the element of Dic 12 can be written in the form ##x^{k}y^{l}, 0 \leq x < 6, y = 0,1##. Write the product between two group elements in the form...
  19. mertcan

    Finite element analysis node displacement

    Hi, I would like to ask why center of element displacement is always estimated with polynomial equation involving nodes displacement (like in attachment/picture)? Also I know that if nodes' number increase for an element then displacement of center of element is estimated with higher order...
  20. I

    Which elements form covalent bonds?

    This might be a very basic question. What are the elements that are in the world of creating covalent bonds, distinguishing themsevels from the elements that never form covalent bonds? Many thanks!
  21. M

    A What is the value of optical effective electron mass for tin

    What is the value of optical effective electron mass for tin metal (white tin)? What is the value of mean free path for electron of tin metal? At least give me some websites or papers where I can find it?
  22. J

    I Line Element in Minkowski Space: Geometric Meaning

    Hello, how can you imagine the geometrically meaning of the minus sign in ds2=-dx02+dx12+dx22+dx32, maybe similar to ds2=x12+dx22 is the length in a triangle with the Pythagoras theorem?
  23. bhobba

    A Bit Of Humor - Heaviest Element Yet Known

    A friend knowing I have an interest in science sent me this amusing story - hope you find it as funny as me Scientists at CERN in Geneva have announced the discovery of the HEAVIEST element yet known to science. It was discovered in Australia, which is now the leading producer, but other...
  24. E

    Finite Element Method: Linear vs. Quadratic Elements & DOF

    Homework Statement Linear and quadratic elements differ because of the extra mid-nodes on quadratic elements. Quadratic elements can "bend", linear can't. How do you define the DOF of a element? (see at solution attempt)Homework Equations - The Attempt at a Solution For example: a linear...
  25. T

    I Invariant element integrand

    Let ##k## be a Lorentz four-vector. The integrand ##d^4k## is the same as ##d^3 k \ dk_0##. Why is this true? ##k_0## is the first component of ##k##. So how are we allowed for equating the two integrands? Just to add context, this situation happens during the construction of the integral for...
  26. P

    [Chemistry] How many electrons an element will gain or lose?

    Homework Statement Predict how many electrons will most likely be gained or lost by each element: In this case, Gallium Homework Equations None (that I know of) The Attempt at a Solution [/B] I know that Gallium is a metal, and metals tend to lose electrons to become cations, so I will...
  27. S

    The emission spectrum of an unknown element

    Homework Statement The emission spectrum of an unknown element contains two lines - one in the visible portion of the spectrum, and the other, ultraviolet. Based on the following figure and what you have learned about Niels Bohr's model of the atom, account for the difference in energy between...
  28. J

    Heat capacity of a heating element, in a flow of air

    Air is flowing through a pipe, through a heater matrix. Flow, Inlet temperature and heater power vary. Is it possible to calculate the heat capacity of the matrix by using the Inlet & outlet temperatures, power & flow? I'm assuming no heat loss to the pipe walls to make it easier, but I'm not...
  29. mertcan

    Studying Finite element analysis for Electromagnetism

    HI, initially I would like to put into words that there are sufficient resources, books or lecture videos on YouTube related to finite element analysis especially for structural dynamics (for instance JURGEN BATHE in MIT). But I would like to make you sure that there NO lecture videos or other...
  30. M

    B Quantum vs. Classical Mechanics in Differential Element Analysis

    When we take a differential element for analysis why don't we consider quantum effects and only consider classical mechanics to solve the problem?
  31. S

    A Reduced matrix element for 0_ --> 0+ forbidden beta decay

    Hello Basically i need some help or references on proving that Working with spherical tensors in a 0_ ---> 0+ forbidden beta decay could you please give me some hints on how to do this proof? Thank you
  32. S

    A Calculation a reduced matrix element using E-Wigner Th.

    Hello. I fail to follow one step in the process of calculating ⟨la∥Y(L)∥lb⟩ . The spherical harmonics Yma(L)(r) represent the 2L+1 components of the spherical tensor of rank L. Writing the Eckart-Wigner th. for M = 0 yields: (1) Also one can write (2) Coupling L and lb to l: (3) Thus...
  33. A

    I Where does the line element of Minkowiski space come from?

    How is it derived? ds^2 =-cdt^2+dx^2+dy^2+dz^2
  34. R

    Resistance of a water heaters heating element?

    Homework Statement Household water heaters use a 240 V rather than a 120 V source. What is the resistance of a water heater's heating element if it heats 40 gallons (151 kg) of water from 15 C to 60 C in 15 min Homework Equations P = IV P = I^2R I = dq/dt The Attempt at a Solution Honestly no...
  35. maistral

    Discussions about Finite Element Analysis (PDFs)

    Hi. Can someone point me to a good (and really basic) PDF file or text regarding Finite Element analysis? I would prefer it having an example where it would solve the 1D heat equation or the Laplace equation so I can extend what I know from finite difference methods to it. Sorry if this seems...
  36. Spinnor

    I Line element from Kaluza-Klein for Kids

    In http://vixra.org/abs/1406.0172, the five-dimensional Kaluza-Klein line element d˜s^2 is given by, Does this look correct? Thanks!
  37. G

    B Can the Half Life of Elements Change in Different States of Matter?

    Just curious , have there been any such circumstances in the history of this universe (i'm thinking close or near the big bang moment of hot dense plasma) or are there possible such a scenario even theoretically where the half lives of isotopes and elements change? In other words for example...
  38. Z

    Quantity of an Element in Mixture by Adding another Element

    Homework Statement A mixture of 12 ounces of vinegar and oil is 40% vinegar, where all of the measurements are by weight. How many ounces of oil must be added to the mixture to produce a new mixture that is only 25 percent vinegar? I don’t know how to solve it. 2. Homework Equations May be...
  39. B

    What is the cause of normal stress on a fluid element?

    In the derivation of Navier Stokes equation there is a term for normal stress acting on the fluid element. While the cause of normal stress is the static pressure which is already present in the equation doesn't this mean that the same force on the fluid element is repeated twice with different...
  40. gimak

    Impedances in a 5 element circuit

    Homework Statement Just help me with 18 b. Homework Equations V1 = c1I1Z1. Same for V2,3,45. V = V1+V2+V3+V4+V5. V/I=Z=impedance. The Attempt at a Solution Maybe because of symmetry Z1=Z2 & Z3=Z4. Perhaps Z5 takes out one of the branches? Can I get a hint?
  41. C

    I What is the hyper-cylindrical line element?

    What is the hyper-cylindrical line element?
  42. G

    I Understanding Isotopes: Exploring the Complexity of Radioactive Elements

    Hello,something I've always had some confusion with is the vast number of radioactive isotopes that form from fission and subsequent decay of the fissioned nuclei. first of all does anyone have a link or something to a good high resolution picture of a chemical elements periodic table kind of...
  43. Asmaa Mohammad

    Target element in Coolidge tube and x-rays

    Homework Statement Homework EquationsThe Attempt at a Solution I would say that the wavelength of the characteristic spectrum will increase, but what about the bremsstrahlung spectrum? Will the cutoff wavelength will be longer?
  44. T

    B Why only certain colors in emission spectrum are visible?

    Why are only certain colors of the emission spectrum in Hydrogen visible?
  45. J

    Making a temperature controlled heating element

    I'm considering making a plastic melter / extruder for making my own 3D printer filament as opposed to buying the spools of it. The basics of the project are simple, but the hard part (for me at least) is making a heating element that has a control on it so that I can turn the heat up or down...
  46. F

    Understanding Finite Element Method: Diagonal Values and Calculating K Matrix

    Homework Statement In the third picture , I don't understand the circled part , add up the values in the diagonal .. How to do that ? I don't understand how to get k13 , k14 , k21 , k22 , k33, k41 and k42 . Homework EquationsThe Attempt at a Solution As we see in the second picture , the k21...
  47. Math Amateur

    MHB 4 Element by 4 Element Multiplication Table ....

    What would be the easiest (but neat and readable) way of entering a 4 element by 4 element multiplication table ... ... for example the multiplication table for the field of 4 elements ... ... Peter
  48. Mr Davis 97

    Showing that an element is not in a field extension

    Homework Statement Let ##K = \mathbb{Q} (1, a_1, a_2, \dots, a_n)##, which is the smallest field containing ##\mathbb{Q}## and ##a_1, a_2, \dots, a_n##, where each ##a_i## is the square root of a rational number. Show that the cube root of 2 is not an element of K. Homework EquationsThe...
  49. davidge

    I Is the Notation for Coordinate Transformation in Relativity Problematic?

    In a change of coordinate system we have ##dx^\mu = (\partial x^\mu / \partial \xi^{\kappa})d \xi^{\kappa}##, where the term in round brackets is the Jacobian. That notation implies a sum over all values that ##\kappa## can take. This don't tell us that it's an alternating sum for the case of...
  50. M

    Electric Element Voltage Specifications?

    Hello, I have a question about electric elements and their corresponding voltages. I am looking at powering a 1500W 120VAC element out of an ordinary kettle with a DC voltage supplied by solar panels. So, from what I understand, 120VAC represents the RMS voltage meaning that it would require...
Back
Top