What is Finite: Definition and 1000 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. Q

    Finite Well Potential - Unbound eigenfunction

    Homework Statement From qualitative arguments, make a sketch of the form of a typical unbound standing wave eigenfunction for a finite square well potential. An unbound particle is one which has total energy E greater than the Potential V of the well Is the amplitude of the oscillation the...
  2. P

    A nonempty set T1 is finite if and only if there is a bijection from T1->T2?

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  3. N

    Learning the Finite Element Method: A Practical Guide for Engineers

    Hi guys I wish to self-study the Finite Element Method. I am mostly interested in learning how to understand and implement the method rather than to investigate if a solution exists, i.e. I wish to follow the "engineering-approach" rather than the "mathematician-approach". Do you have any...
  4. F

    Designing a DFA for L={vwv : v,w elements of {a,b}* and |v| =2}

    L={vwv : v,w elements of {a,b}* and |v| =2} I know that "v" can take either aa, ab, ba or bb as values. I also know that "w" can be any string containing "a" and "b". Overall, I know that the two first and two last characters must be identical. How would I show this in a DFA or even an NFA...
  5. Q

    Finite Element Convergence Analysis

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  6. B

    Electric field due to a finite and infinite sheet of charge.

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  7. ¡

    Magnetic Field Outside of Finite Solenoid Greater for Air-Core or Ferrite-Core?

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  8. quasar987

    Free finitely generated module has finite rank?

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  9. A

    Axiom of Choice: finite sets to infinite sets

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  10. S

    How Does MATLAB Implement Finite Element Method for Modified Poisson's Equation?

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  11. camipol89

    Particle falling into a black hole singularity within a finite proper time

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  12. E

    Extension of Finite Fields: Proving the Number of Elements in F(\alpha)

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  13. T

    Multi-region Finite Difference- Interface between materials

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  14. Y

    A subspace has finite codimension n iff it has a complementary subspace of dim nu

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  15. E

    Every element of a finite field is a sum of 2 squares?

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  16. F

    Finite potential well easy question

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  17. R

    Boundary conditions in finite potential well

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  18. G

    Electric field due to a finite line of charge

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  19. A

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  20. T

    How can Block Holes form in finite time?

    I think this subject may have been discussed here already; please point to the thread if so. I am unable to understand how Black Holes can form within the lifetime of the universe. If nothing can cross an event horizon in finite time, then it seems clear that the horizon can't form (at...
  21. S

    Is our universe finite or infinite?

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  22. B

    Why can finite elements handle complex geometries, but finite differences can't?

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  23. B

    Fast Construction of Irreducible Polynomials of degree n over any Finite Field

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  24. B

    Fast Construction of Irreducible Polynomials of degree n over any Finite Field

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  25. M

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  26. D

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  27. S

    F uniformly continuous -> finite slope towards infinity

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  28. J

    There exists a set of all finite sets?

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  29. M

    What is the Finite Field Order of Z[i]/A in Z[i] with A=<1+i>?

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  30. C

    Solving Diffusion PDE By Finite difference Method in fortran

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  31. C

    Solving Diffusion Equation By Finite difference Method in fortran

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  32. P

    Finite cartesian product of connected space is connected

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  33. I

    Setwise stabilizer of a finite set is a maximal subgroup of Sym(N)

    So I'm reading a paper which assumes the following statement but I would like to be able to prove it. Let S denote the symmetric group on the natural numbers. If \emptyset\subset A \subset \mathbb{N} then S_{\{A\}}=\{f\in S:af\in a,\;\forall{a}\in A\}$ is a maximal subgroup of S...
  34. I

    What is the unidimensional case of a finite barrier inside a finite well?

    After hours searching the web I was not able to find the unidimensional case "a finite barrier inside a finite well". I would appreciate if someone could give me a reference about it.
  35. W

    A comprehensive book for finite element methods ?

    I am doing BE in mechanical engineering. I'm looking for a comprehensive book on finite element methods preferably with a lot of solved numericals . Suggestions, please?
  36. S

    Eigenvalues of a linear map over a finite field

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  37. H

    Finite Difference Discretization of a Fourth Order Partial Differential Term

    What is a finite-difference discretization for the partial differential term: \frac{\partial^4\phi}{\partial x^2\partial y^2} Thanks in advance.
  38. A

    Ultimate size of the Universe (finite)

    Ok, I am a mechanical guy, mechanical engineering degree. With an argument with my Engineering physics wife. 1. Imagine 2 particles (lightest particle with any finite mass) 2. separated by the the entire distance of the universe 3. the particles are attracted (due to gravity) to each other...
  39. L

    Countable vs Finite Rationals in (0,1)

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  40. G

    Proving Exponent of Finite Groups Divides Order

    Homework Statement prove that every finite group has exponent that divides the order of the group Homework Equations The Attempt at a Solution Given G is a finite group and x \in G. Suppose x has order m, then <x> = {e,x,x^2...x^(m-1)} and so \left|<x>\right| = m so by...
  41. L

    Gamma Rays: Finite Range in Water?

    i was told that high emergy gamma rays had a finite range in water. how can this be if they are both massless and chargeless. is it because they are absorbed/produce electrons/positrons thanks
  42. V

    Finite quantum well, factor of 2*pi seems necessary but why?

    Homework Statement Solve for the allowed energy values E of a finite square quantum well of depth U0 = 25eV, width a = 0.5nm that contains an electron of mass m (I'm presuming that m = 9.11*10^-31kg, the question doesn't indicate a specific value to use). I'm defining the interior potential to...
  43. S

    Neumann Condition on Curved Boundary using Finite Difference

    Hi, I am trying the solve the Poisson equation in a domain with curved boundaries using the Finite Difference Method (second order accurate). I need to apply the Neumann condition on the curved boundary. I have used bilinear interpolation to do this but this causes the resultant scheme to be...
  44. S

    Finite potential well- well's depth?

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  45. S

    Point charge and finite dielectric slab

    Hi All, I want help to solve a problem: A point charge is placed at a distance 'L' from the surface of an infinite dielectric slab (permittivity: k1 and thickness 'd'). The entire region of space (outside the slab has a permittivity k2). First, I need to solve for the energy of the system...
  46. M

    Examples of martingales that oscillate between finite values infinitely often.

    Homework Statement Find an example of a martingale (X_n, (\mathcal{F}_n)_{n=0}^\infty, P) such that P(X_n = a \mbox{ } i.o.) = 1 for a = -1, 0, 1 and sup_n X_n < \infty . (i.o. = infinitely often) Homework Equations We must have sup_n X_n < \infty . The Attempt at a Solution...
  47. S

    Finite Integral in measure theory

    Hello, I am preparing for a screening exam and I'm trying to figure out some old problems that I have been given. Given: Suppose \mu is a finite Borel measure on R, and define f(x)=\int\frac{d\mu(y)}{\sqrt{\left|x-y\right|}} Prove f(x) is finite almost everywhere If I integrate I...
  48. T

    A problem in Finite Group Theory

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  49. N

    Finite Element vs. Finite Volume

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  50. D

    Finite element analysis software

    i am a 3rd year civil engineering student, currently taking a course in which i need to use finite element software for assignments. the course is 100% theory, and i need to learn how to use the software on my own, i am looking for FREE software with FE capabilities, and preferably one that...
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