Questions tagged [finite-element-method]
Usage of the Finite Element Method embedded in NDSolve and details on the implementation of the fem in mathematica.
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Solving a coupled 2nd order differential equation numerically using NDSolve
I would like to solve the following system of differential equations numerically for two one-dimensional functions $R(x)$ and $\phi(x)$:
\begin{eqnarray}
c_1 \left(R''(x) - (\phi'(x))^2 R(x) \right) - ...
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Why Interpolation with InterpolationOrder -> 1 looks smooth in 2D case?
The following code
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Oblique derivative boundary conditions in FEM
In one of my tasks, it is necessary to set a boundary condition in the form of an oblique derivative for the two-dimensional Laplace equation.
Do you know how this can be done in Wolfram Mathematics? ...
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Machine number overflow when solving a PDE system
Recently I asked a question on solving a system of 3 nonlinear PDE (To solve a system of 3 nonlinear PDE). Now I transitioned to the next step, that is, a realistic PDE which has been my initial aim:
<...
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To solve a system of 3 nonlinear PDE
I am trying to solve a system of 3 nonlinear partial differential equations:
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Heat equation with b.c. at $+\infty$ and i.c. at $-\infty$
I am wondering what is the best way to solve numerically a initial-boundary value problem of heat equation like this (surely I've made a lot of mistakes in the code):
...
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NDSolve exceedingly slow
I the following ODE with parameters
\begin{align}
B_e\: \theta''(s)+2(s-1)\cos\theta(s)=S_e\: f\left(\theta(s)\right),
\end{align}
with $0\leq s\leq 1$ and
\begin{align}
\theta(0)=0\:\:\:\text{and}\:\:...
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Can't evaluate and plot eigenfunctions after using NDEigensystem
I used NDEigensystem for finding eigenvalues and eigenfunctions of specified dif. operator. If I set R=1 everything is good and I get right results, but when I set R=10 and more I get complex ...
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Can we construct 3D meshes that respect internal boundaries?
In a recent answer to a question on constructing 2D meshes with internal boundaries @user21 provided an extremely useful answer which can be found here.
I have tried to extend this to 3D by ...
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How to Solve PDE using Inactive Form
I am trying to solve this PDE using the inactive form, however I ran into error stating that the: The PDE coefficient 0....
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Mesh Rectangle with a fixed inner Line
In this simple example I try to mesh a rectangle, the mesh should include a fixed line.
Using "IncludePoints" I get
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PDE in inactive form
I am trying to solve this complex PDE, however I am getting an error from Mathematica stating: The maximum derivative order of the nonlinear PDE coefficients for the Finite Element Method is larger ...
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Solving Poisson's Equation Numerically
I'm trying to numerically solve Poisson's equation for the following scenario:
The potential inside a cylinder of radius R=1 and height H=2 with uniform charge density(which I'll set to 1).
Poisson's ...
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Speed up a finite element solver with small features (full code without error)
This is a question similar to the previous one with small features. I'm solving this problem by modifying the method of @Alex. The code can run without error, but it was always stuck at ~...
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How can I color a cylinder inside a sphere?
I am trying to draw a figure and color it like this from here:
I tried
CSGRegion["Difference", {Ball[{0, 0, 0}, 5], Cylinder[{{0, 0, -5}, {0, 0, 5}}, 2]}]
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