New answers tagged finite-element
10
votes
Electromagnetic Eigenvalue problem in FEM yielding spurious solutions
You are correct, this formulation does introduce a spurious space. It's not actually due to any function space/discretization choice, but rather that change of variables step ($\mathbf e_t = k_z \...
- 5,046
2
votes
Jacobian of 2D element in 3D domain
I think the most general and elegant approach is to use a pseudo-inverse. The Jacobian, in general, is of size $n \times m$, where $n$ is the physical dimension of the domain/mesh, and $n$ is the ...
- 31
1
vote
Jacobian of 2D element in 3D domain
The Jacobian in 2D and 3D is respectively defined as
$$J^e=\begin{bmatrix}
\dfrac{\partial x}{\partial\xi}&\dfrac{\partial y}{\partial\xi}\\
\dfrac{\partial x}{\partial\eta}&\dfrac{...
- 433
2
votes
L2 bounds for fem local basis functions
The inequality at the top is known as an "inverse inequality". Basically, it says that if you squeeze a shape function from the reference cell into a cell of size $h$ (relative to the ...
- 56.2k
1
vote
Finite element accuracy on non-affine quadrilateral meshes
Case of quad meshes
Let us take exact solution to be $\psi = 1 + x + y + xy$. Then $\psi$ satisfies
$$
a(\psi,\phi) = 0, \qquad \forall \phi \in H^1_0
$$
with $\psi$ taking prescribed boundary values.
...
- 3,038
3
votes
Shape functions on the triangle using vertex values and derivatives
For a quadratic polynomial in 2D you need $1$ coefficient for the constant term, $2$ coefficients for the linear term, and $3$ for the quadratic terms, for a total of $6$ coefficients. For a cubic you ...
- 2,352
4
votes
Accepted
Finite element accuracy on non-affine quadrilateral meshes
This is too long to be a comment, so I will leave it here as an answer.
There are two issues here preventing $\psi_h$ to be exactly equal to $\psi$. The first issue has to do with the nature of the (...
- 176
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