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. evinda

    MHB If there doesn't exist any other element at the list, what do we do?

    Hello! (Wave) I want to write a $O(n \lg k)$ time algorithm in order to merge $k$ sorted lists into one sorted list, where $n$ is the total number of the elements in all the input lists. I tried the following: We create an array with k elements, where $A[i]$ is the firstunused element of...
  2. S

    Question about the periodic table arrangement

    Hi, I'm new here. I'm actually studying the periodic table and while collectting the data on excel i noticed something. I wouldn't see it with the usual display of a periodic table but when you put it all in a sheet, ligns after ligns it become obvious to me. Argon Ar (noble gaz) is followed...
  3. M

    Need to find the length and deflection of bending element

    Hi, I have a task and don't know the good solution. (I add the picture of my task.) I need to find the right length and deflection and to check if the results didn't exceed the allowable stress. I know the value of "q" (force). Also I could choose myself the lenght, but I need to check, if my...
  4. Calpalned

    Is half-life inversely related to the radiation dosage of an element?

    Is half-life inversely related to the radiation dosage of an element? That is, if an element has a longer half-life is it safer? If so, why is plutonium so dangerous, even though it has a very long half life
  5. Calpalned

    Two atoms of an element with a half life of ten years

    On the other hand, what if we only have two atoms of an element with a half life of ten years. Then after then years, only one atom of that original element remains. What happens next? Is the lone surviving atom immutable?
  6. C

    When is integral closure generated by one element

    Hello, This is not a homework problem, nor a textbook question. Please do not remove. Is there a concrete example of the following setup : R is an integrally closed domain, a is an integral element over R, S is the integral closure of R[a] in its fraction field, S is not of the form R{[}b{]} for...
  7. CivilSigma

    Is the decay constant , constant for all isotopes of element

    I have this true and false question: " The half life and therefore the decay constant will be the same for every isotope a) True b) False c) only if it is an isotope of the same element " I think this is false, just by intuition.
  8. evinda

    MHB Understanding AVL Tree Rotations: Solving the Case RL

    Hello! (Smile)We want to insert $58$ at the following AVL-tree and then we have to make rotations so that the tree is balanced. According to my notes, we are at the case RL (The first edge leads to the right and the second to the left), where two rotations are required, one right around the next...
  9. evinda

    MHB Find Next Smallest & Greatest Key in BST

    Hello! (Wave) We consider a Binary search tree and we want to find the element with the next greatest and the next smallest key than the key of a node v. For example, how can we find the next of the node to which q1 points in the in-order traversal? How will we find the next of the node to...
  10. evinda

    MHB Algorithm to Find Element of Order k in $\Theta(n)$

    Hello! (Wave) We are given the function β-select(A) that gives as an output the position of the $\lfloor \frac{n}{\beta} \rfloor$-th element in time $\Theta(n)$, where $n$ is the number of elements of $A$. I want to write an algorithm that returns the element of order $k$, $1 \leq k \leq n$ of...
  11. G

    Voltage required for penetration of an unknown element

    Homework Statement An unknown element has a nucleus with charge 14.00 e and a radius of about 3.60×10-15 m. How much voltage must be used to accelerate a proton (radius 1.20×10-15 m) so that is has sufficient energy to just penetrate the unknown element? Assume that the potential is that for...
  12. Ahmed Abdullah

    Rubik's cube group element with the smallest order

    Wikipedia says that largest order of any element of Rubik's cube group is 1260 [PLAIN]http://upload.wikimedia.org/math/e/1/c/e1cff178a2562422492a4140a38f93ff.png. http://en.wikipedia.org/wiki/Rubik%27s_Cube_group What about element of smallest order (except the identity element)? I'll...
  13. T

    Expression for the line element ds^2

    ds2=guvdxudxv Why is the invariance of ds2 as shown above? Why can't it be something like ds2=guudxudxu or ds2=dxudxu ? Isnt it based on Pythagoras theorem? Why must it have 1 u and 1 v instead of just 2 u or 2 v? Forgive me for such dumb question as I just started.
  14. Ahmad Kishki

    What assumption leads to dB/dt=0 in the lumped element model?

    First assumption: the change of magnetic flux in time outside a conductor is zero. Last semester in circuit analysis we treated circuits with sinusoidal voltage variation as steady state circuits while using the phasor notation. But now that i know electrodynamics i begin to doubt my concepts...
  15. N

    How Does the Momentum Operator Act in the Matrix Element <pm|p|pn>?

    Can somebody explain how you get: <pm|p|pn> = (1/2π)∫e-ipmx/h (-ih∂/∂x) eipnx/h dx ... = ih∂δ(pm - pn)/∂x Conceptually, I am having a problem with how the inner product is formed when a derivative is involved (i.e. the ... steps)
  16. evinda

    MHB Finding the $j^{th}$ Smallest Element in an AVL Tree

    Hello! (Wave) We consider an $\text{ AVL }$ tree $T$. At each node $v$ of the tree the number of nodes of the left subtree of $v$ is stored. I want to write an algorithm that returns the $j^{th}$ smallest element of the tree in time $O(\log m)$ where $m$ is the number of nodes of the tree. How...
  17. N

    Every known element has a unique atom?

    This notion perplexes me. Could I please have this explain with an example(s). I am confused are atoms not made up of the same protons and neutrons which are just essentially negatively or positively charged particles which are made of quarks? Which as confusing as that can become. How can one...
  18. DivergentSpectrum

    Surface element -- why parallelograms?

    we say the surface element of x(u,v),y(u,v),z(u,v) is absolute value of the cross product or i don't understand why this is. i know that the absolute value of the cross product is the area of a parallelogram formed by a,b,a+b, but i get lost after that im guessing something happens where dudv...
  19. U

    How is the Faraday Tensor related to the 4-potential?

    The Faraday Tensor is given by: Consider the following outer product with the 4-potential: The Faraday Tensor is related to the 4-potential: F^{mn} = \Box^{m} A^n - \Box^n A^m For example, ## F^{01} = -\frac{1}{c} \frac{\partial A^x}{\partial t} - \frac{1}{c}\frac{\partial...
  20. P

    MHB Separable Element: Minimal Polynomial Question

    if a\inK be seperable element over the field F,let f(x) be minimal plynomial of a over F.let degree of f(x) be n, We know f(x) will be seperable over F, BUT is it necessary that f(x) will be MINIMAL POLYNOMIAL of other n-1 roots. if so, what is the reason?
  21. evinda

    MHB Finding Min. Element in Sequence: Algo & Steps

    Hello! (Smile) We have a sequence of numbers $A=(a_1, a_2, \dots, a_n), n \geq 3$, for which, it stands the following: $$\forall i \text{ with } 2 \leq i \leq n-1:$$ either $$ 1. a_{i-1}<a_i \text{ and } a_i>a_{i+1}$$ or $$2. a_{i-1}>a_i \text{ and } a_i<a_{i+1}$$ I have to write an...
  22. evinda

    MHB Find Min Element in A Sequence w/ $O(\log n)$ Complexity

    Hello! (Nerd) A sequence of numbers $A=(a_1, a_2, \dots, a_n)$ is called convex if there is a $k$ with $1 \leq k \leq n$ such that $\forall 1 \leq i \leq k-1$, we have that $a_i>a_{i+1}$ and $\forall k \leq i \leq n-1$ we have that $a_i<a_{i+1}$. Write an algorithm with time complexity $O(\log...
  23. B

    Making stable element unstable

    A simple answer I got searching the web to as why we can't split atoms of non-radioactive elements is that they are stable.So,why can't we make stable elements unstable(radioactive)? Is this possible at least in theory?
  24. T

    Finding Force in Element D-C of a Truss

    Homework Statement I've solved all but one force. I can't seen to get the force within element D-C. All relevant variables are shown on the pics attached i.e loads, supports, dimensions etc... Homework Equations Sum of forces in x=0, sum of forces in y=0, sum of moments=0 on Here are links...
  25. H

    Exploring One-Sided vs. Two-Sided Identity Elements in Groups

    Hi I'm taking a math course at university that covers introductory group theory. The textbook's definition of the identity element of a group defines it as two sided; that is, they say that a group ##G## must have an element ##e## such that for all ##a \in G##, ##e \cdot a = a = a \cdot e## ...
  26. M

    MHB Can a Single Complex Number Generate the Splitting Field of \(x^3-2\)?

    Hey! :o Let $E$ the splitting field of $x^3-2 \in \mathbb{Q}[x]$. Applying the algorithm of the proof of the Primitive element theorem, find a complex $c$ with $E=\mathbb{Q}(c)$. I have done the following: The splitting field is $E=\mathbb{Q}(\sqrt[3]{2}, \omega_3)$. Since $\sqrt[3]{2}...
  27. J

    [Antenna Beam Forming] Antenna Pattern & Element Pattern

    Hey guys, currently I am working on my diploma thesis in the field of beam design for mobile communication. I created a linear array with N elements and computed the corresponding Array Factor with the help of the chebyshev distribution. I assume my Element Factor to have its maximum at 90°...
  28. evinda

    MHB Using a Sentinel Value to Find an Element in a List

    Hi! (Smile) If we want to look for an element $x$ in a list, we can use a sentinel value. What do we gain, with the use of a sentinel value?
  29. B

    Calculating the order of an element in cycle notation

    Homework Statement Let ##g \in S_n## and suppose that we know the cycle notation for ##g##. How can one compute its order without repeatedly composing ##g## with itself? Homework EquationsThe Attempt at a Solution [/B] I took the group ##S_4## and tried formulating a conjecture. I composed...
  30. genxium

    How is (d^3)r in Green's Function equivalent to volume element?

    Homework Statement This is part of the online tutorial I'm reading: http://farside.ph.utexas.edu/teaching/em/lectures/node49.html I'm so confused about the notation of Dirac Delta. It's said that 3-dimensional delta function is denoted as \delta^3(x, y, z)=\delta(x)\delta(y)\delta(z) in...
  31. S

    Calculating a matrix element & first order shift

    So I saw this a moment ago: How can the second and third terms yield (n+1)+(n-1)=2n and not (n+1)+n=2n+1? PS: I solved the problem by using [a,a(+)]=1. Sorry, this is very simple but I cannot figure out what I did wrong.
  32. C

    Properties of a supernatural element?

    If you had to a create a super element to be added to the periodic table, what would it be? I'm talking about it's properties.. give me some good techno babble.
  33. K

    About diagonal element of dipole

    Hi all, I am reading a book on atom interaction with light. It starts with the 2 level system. The book said the diagonal elements of dipole operator is zero, i.e. ##\langle g|x|g\rangle = \langle e|x|e\rangle = 0##. I don't understand why this is true but after searching online and there...
  34. C

    Current Divider Formula if R for element = 0

    Hi I was wondering say for example you had this simple current divider circuit. I was wondering if R1 for example had zero resistance it would have all current dropped over it. However pertaining to the current divider formula. ##I_i = Is (R_T / R_i)## Thus if R1 = zero the equation is not...
  35. S

    Examples of A intersection B being an element of A

    What are some examples where the intersection of two sets is a member of one of the sets? Let A,B,C,D be sets whose elements are sets of integers. A = \{\emptyset, \{1,2\},\{3\} \} B = \{\{4,5,6\},\{7,8\} \} C = \{ \emptyset, \{7,8\} \} D = \{ \{3\}, \{4,5,6\} \} Then A \cap B =...
  36. B

    Order of an element in a group

    Hello everyone, I am working with an arbitrary finite group ##G##, and I am trying to prove a certain property about the order of an arbitrary element ##g \in G##. Supposedly, if we are dealing with a such a group, then ##o(g)##, which is the cardinality of the set ##| \langle g \rangle |##, is...
  37. evinda

    MHB Both fields point to the same element

    Hello! (Wave) Given the following two lists: what could we do, so that the first list contains both the elements of the first and the second list, sorted? (Thinking) I wrote the following algorithm: pointer *P=L1, *Q=L2,n; while ((P != '\0') && ( Q != '\0')){...
  38. S

    Which element has "stronger" radiation?

    Sorry if I am asking a stupid question. I recently had an argument with my friend which among this two is more dangerous: 3H or 235U(not considering its decay chain products). I was under the impression that 3H has an effective dose about 1000 times smaller than 235U due to its weak...
  39. J

    Heating Saline with an Element: Is it Possible?

    Hi there. Is there any element, when exposed to saline, will cause the saline to heat up? More to the point, I would like to add something to a jar of saline and heat it up. Is that possible? Thanks, ~J
  40. L

    Determining when a function is an element of L^2 (0,1)

    Homework Statement Determine for what k f(x)=xk is an element of L2 (0,1) vector space k ∈ ℝ Homework EquationsThe Attempt at a Solution \int_{0}^{1} x^{2k} dx = \frac{1-0^{2k+1}}{1+2k} = \sum_{n=0}^{\infty}{(-2k)^{n}} (for k > -½) This sum should converge for \lim_{n \to +\infty}...
  41. M

    MHB Proof: $K[a]$ is a Field & if $K(a)=K[a]$, then $a$ is Algebraic Over $K$

    Hey! :o $K \leq L, a \in L$ I am looking at the proof that if $a$ is algebraic over $K$, then $K(a)=K[a]$. We show that $K[a]$ is a field, then we have that $K \subseteq K[a] \subseteq K(a) \subseteq L$. Let $0 \neq c \in K[a]$, then $c=f(a), f \in K[x]$. Let $p(x)=Irr(a,K)$. Since...
  42. evinda

    MHB Why can it consist of only one element of a?

    Hey! (Nerd) If $a,b$ sets, then we symbolize $\{ a,b\}$, the set that has as elements $a$ and $b$ and only these. If $\{ a, b \}$ a set of pair and $a=b$, then we write $\{a,a \}=\{a \}$ and the set $\{ a \}$ is called the singleton, that consists of only one element of $a$. Why can $\{a\}$...
  43. M

    Proving each nonzero element of a subfield of C has an inverse

    Homework Statement Let S={p+qα+rα2 : p, q, r \in \mathbb{Q}}, where α=\sqrt[3]{2}. Then S is a subfield of \mathbb{C}. Prove that each nonzero element of S has a multiplicative inverse in S. The Attempt at a Solution Let p, q, r\in\mathbb{Q} such that not all of p, q, r are zero. If...
  44. Jarvis323

    What is the precise definition of, "Differs in exactly one element"?

    Do {1,2,3} and {1,2} differ in, or by exactly one element? Or do those two things mean the same thing. Also, what about {1,2,3} and {1,2,4}.
  45. evinda

    MHB Find the second smallest element

    Hi! (Nerd) Show that,given a set of numbers $S$,we can count the second smallest element of $S$ with $n+ \lceil \lg n \rceil-2$ comparisons at the worst case. Hint: Find the smallest element,considering a tournament tree for its finding. I don't really know how to use the hint.. (Sweating)...
  46. Chacabucogod

    Solving the Finite Element Method Matrix with Rao - Engineering

    I was reading the finite element method in engineering by Rao and in the first example he ends up with a matrix that is singular. The matrix is the following: \begin{pmatrix} 2 &-2 & 0\\ -2 & 3&-1\\ 0&-1& 1 \end{pmatrix} Which is a symmetric matrix as far as I can remember...
  47. M

    Let S be the subset of group G that contains identity element 1?

    Homework Statement Let S be the subset of group G that contains identity element 1 such that left co sets aS with a in G, partition G .Probe that S is a subgroup of G. Homework Equations {hS : h belongs to G } is a partition of G. The Attempt at a Solution For h in S if I show that hS is S...
  48. D

    Conceptual questions on proving identity element of a group is unique

    Hi, I'm hoping to clear up a few uncertainties in my mind about proving that the identity element and inverses of elements in a group are unique. Suppose we have a group \left(G, \ast\right). From the group axioms, we know that at least one element b exists in G, such that a \ast b = b \ast...
  49. S

    Potential Energy Approach to Derive Spring Element Equations

    Good day! I am a beginner in Finite Element Analysis and Structural Mechanics. I have problem in understanding the insight of potential energy approach to derive spring element equations. I have already search for similar post and I found this, and agree with the example raise...
  50. N

    Is there any element that does not absorb neutrons?

    Recently I have been researching the topic and I have not found any completely clear answer. To restate my question (as I asked in the title), is there any element that would not absorb neutrons and if not which element has the lowest neutron absorption rate? Thank you.
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