A method of obtaining (numerically) approximate solutions to (usually) differential equations. It consists of a method of discretization splitting the domain into disjoint subdomains over each of which the problem has a simpler (approximate) solution, and a method of reassembling those pieces to obtain a solution over the whole domain. It is closely tied to the calculus of variations.
Questions tagged [finite-element-method]
637 questions
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inf-sup condition (Finite Element)
I have a question about inf-sup condition. In these at page 14 is explained the Mixed Formulation in Mixed Finite Elements. We can re-write the problem in this way: let $A:V\to V^\ast, B:V\to Q^\ast, K = \operatorname{Ker} B\subset V, F\in…
Eleonora
- 87
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Difference between Continuous and discrete setting in Finite Element Method
I often hear the lecturer making comparisons between continuous and discrete setting in FEM (topics related to Poisson equation Mixed FEM). My vague understanding is that it is impossible to find a solution in the continuous setting, hence we…
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Finite elements for biharmonic equation
I have a question regarding the conforming finite elements for biharmonic equation: if we want to discretize the weak formulation for this problem using a conforming finite element space $V^h$, is it possible to do it using Lagrange elements? If…
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FEM approach to obtain the projection of a function onto the mesh?
I need to explain the background of the problem I'm working on, and the questions themselves are a couple of paragraphs down. I am reading this book and implementing the algorithms along (so far in chapter one, assemble the mass matrix and the load…
J.P.
- 168
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Data transfer in the context of adaptive mesh in finite element method (FEM)
In the context of adaptive mesh in FEM, after a new mesh is created, the data on the old mesh are to be transferred to the new mesh. For the data on the integration points (IPs), it seems the usual way is to (1) transfer the data on IPs of the old…
Riche
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A question on the FEM method
In the Finite element, we take a function with free parameters and put it into an equation, but it doesn't solve this equation, so why don't we get $0=1$?
Why does this method give an approximate solution?
If I have the equation $2*f(x)^2=x$, and…
badmf
- 390
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1 answer
Implementing Neumann boundary condition for elasticity problem using the finite element method
I am solving the following mixed boundary elasticity problem with the finite element method on the unit circle, using a triangle mesh with 3 nodes on each element:
$ \frac {\partial}{\partial x_j}\sigma_{ij}(u(x_1,x_2))=0 $, $(x_1,x_2) \in \Omega$
$…
Rebekah
- 13
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What's an exact geometry?
Some papers (eg1., p. 2980) on isogeometric analysis talk about some geometric being exact or some geometry being expressed exactly.
The paper also says that
However, as NURBS patches (of higher order) are capable of
representing most geometries…
mavavilj
- 7,270
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Showing an inequality on the interpolant error
I have established the inequality $ \|u'-U_{I}'\| \leqslant c_\alpha h\|u''\|$
where $U_{I}$ is a piecewise linear interpolant on $[a,b]$ and $h = \max_{i} x_{i+1} - x_{i}$. Recall the Poincare-Freidrich (PF) inequality:
$$ \|f\| \leqslant c…
clocktower
- 1,447
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Finite error estimate on non-convex domain
Let $\omega \in (\pi, 2\pi)$ and $\Omega=\{(r\cos\phi, r\sin \phi); 0
Marko Rajkovic
- 133
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Possion equation
Poisson's equation with Robin boundary conditions:
−Δu=f in $\Omega=]0,a[\times]0;b[ $
$\alpha u$+$\frac{∂u}{∂n}$=g $in \; \Gamma$.
for a given f$\in L^2(\Omega)$,g$\in L^2(\Gamma)$,$\alpha \in L^\infty(\Gamma), \alpha(x,y)\ge 0$
the existence…
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Shape function in Finite Element Method
Why is it that the choice of polynomial for 6-nodes rectangular element(linear in sides 1 and 3, quadratic in sides 2 and 4) in FEM does not follow normal pascal triangle regular arrangement? i.e $u=c_1+c_2x+c_3y+c_4xy+c_5xy^2+c_6x^2y$ .
