# 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 PDE for Diffusion Equation (Boundary Condition Issue) [duplicate]

I am trying to solve this partial diffusion equation shown ...
39 views

### Numerical instability due to convection dominated PDE [duplicate]

I am trying to solve this partial diffusion equation shown ...
1 vote
143 views

### Numerical solving diffusion equation in spherical coordinates

Mathematica nicely solves Poisson's equation in spherical coordinates as ...
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### How to mesh a cylinder with helix points?

I would like to mesh a cylinder surface. The mesh should include given cylinderpoints which lie on a helix. My attempt using "IncludePoints" ...
133 views

### Numerical ground state wavefunction of Schrödinger equation with a Coulomb potential in 2D from NDEigensystem

I want to numerically solve the ground state wave function of the hydrogen atom with the Coulomb potential using the NDEigensystem. Here is the code to get the ground state wave function from the ...
278 views

### Minimal surface bounded between turns of helix

I'm curious to find the shape of a surface bounded between the rungs of a helix, ie the shape of the cloth stretched between the rungs of this child's play tunnel. I'm wondering if we could find it ...
134 views

### Problem with pdetoode for two coupled PDEs

I tried to adapt a code for a single equation to solve the following system using 'pdetoode' Updated answer ...
143 views

### Solving system of first order PDEs

I am trying to solve the 1st order PDE system \begin{align} \xi_u^2+\eta_u^2&= \left(1+\frac{\xi^2+\eta^2}{4} \right)^2\\ \xi_v^2+\eta_v^2&=\left(1+\frac{\xi^2+\eta^2}{4} \right)^2 \end{align} ...
255 views

### Numerical solution of second-order linear hyperbolic PDE

(I'm also searching for analytical solutions to this PDE; check the bountied questions here and here if you have any ideas) I'm trying to find the numerical solution of the following 2D second-order ...
196 views

### Machine overflow when defining boundary conditions

Recently I have been trying to code Maxwell's equations over a closed surface and have been facing some trouble defining the boundary conditions for the magnetic field. The equation for the normal of ...
100 views

### Solving Poisson PDE with NDSolve and incomplete BC specifications

When solving the following PDE with a missing BC on the fourth edge ($y=1$): ...
167 views

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### Can Mathematica's FEM solve coupled Dirichlet Boundary Conditions?

I am solving a coupled system of PDEs using Mathematica's FEM capabilities. Specifically, the Navier-Stokes equations with a no-flux stress-free boundary. To do this, I need to specify a Dirichlet ...
1 vote
130 views

### Why does NDSolve solution not match physical intuition?

Related to a previous question I posted, I am trying to solve for the electric potential on a box which obeys Ohm's law: \begin{equation}\nabla\cdot(\overset{\scriptscriptstyle\leftrightarrow}{\sigma}...
1 vote
147 views

### How to calculate a numerical Fourier transform obtained from NDSolve?

We numerically solve for the electric potential on a box which obeys Ohm's law: \begin{equation}\nabla\cdot(\overset{\scriptscriptstyle\leftrightarrow}{\sigma} \nabla \Phi) = 0, \label{Eqn:OhmsLaw}\...
1 vote
207 views

### Normalization of solution of a PDE

I am trying to solve the following PDE: pde = D[P[x, t], t] + D[J[x, t], x] == 0; ...
274 views

### Area, perimeter and other geometric parameters of a "cucumber"

From the simulation, I have got a region with a shape of a cucumber. Here are the boundary points of this region: ...
1 vote