# Questions tagged [finite-element-method]

Tag for the usage of "FiniteElement" Method embedded in NDSolve and implementation of finite element method (fem) in mathematica.

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### NDEigensystem to solve differential equation

When trying to solve the differential equation radialEqdouble[k_] = f''[u] + k*u^2*f[u] - u^4*f[u] where k is a constant, I am able to produce a plot consistent ...
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### Identify the Vertices and Lines around the edges of a free surface - Mesh/DiscreteGraphics

To write a mesher that closes a mesh surface using an implied surface from a boundary spline curve and mesh generated using DiscreteGraphics, I need to identify the Vertices and Lines around the edges ...
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### InitializeBoundaryConditions::fembdnl: The dependent variable in the boundary condition needs to be linear [duplicate]

Checking the documentation on the error were of not that much help to me. Can someone please suggest how to deal with it? ...
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### Closing Boundary Mesh with closed 3D Spline Curve

I am trying to make a 3D solid (with BoundaryMeshRegion) from surfaces created by spline curves. In the follow simple example, I need to close the ends of this irregular tubular shape using boundaries ...
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### Create a “loft” surface from two BSplineCurves?

Is there a way to take two arbitrary BSplineCurves and create a loft surface? I would like to then create a mesh to send to NDSolveValue.
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I want to create graded mesh inside a cube, with finer mesh in the left half and a coarser mesh in the right half. My plan was to partition the cube with a 2D plane and then generate boundary mesh ...
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### Solving a Modified Biharmonic Equation on a Square

I am seeking to solve the differential equation \begin{equation} \left[\partial_{\overline{x}}^{4}+2\left(1+\delta\right)\partial_{\overline{x}}^{2}\partial_{\overline{y}}^{2}+\partial_{\overline{y}}^{...
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### Solving heat equation on a cylinder with insulated ends and convective boundary conditions

I am trying to solve heat equation on a cylinder whose ends are thermally insulated and its circular face is exposed to convection. Therefore I have Neumann boundary condition on all faces of the ...
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### FEM analyis of flow in a hydrocyclone [closed]

I am interested in solving the flow in a hydrocyclone (steady Navier Stokes equation). I have an STL file of the 3D geometry. My question is how to extract the internal geometry of the hydrocyclone ...
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### eigenvalue and eigenfunction of complex euler-bernoulli beam

So I am new to Mathematica and am trying to solve the euler-bernoulli modal equation for a U-shaped Cantilever beam given by equations :- where i is the index of the region. In total there are 2 ...
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### Time dependent Schrödinger equation in 2D

I have the following Schrödinger equation in $2D$: \begin{cases} \partial_t \Psi(x,t) = V(x,t) \Psi(x,t) \quad x \in [-10,10]^2\\ \Psi(x,0)=\exp( \frac{1}{2} (-x^2+y^2)) \end{cases} where the ...
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### NDSolve for system of PDEs -Error: fewer dependent variables!

I am trying to solve the equations below to find the breakthrough curve in an adsorption process: ...
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### ToElementMesh Error/General meshing strategies

I am trying to create a mesh using ToBoundaryMesh as opposed to DiscretizeRegion. I was hoping this would be a better strategy ...
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### Periodic extrapolation out of the domain of the solution of a PDE in two directions

As a prototypic problem ...
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### Improving mesh and NDSolve solution convergence

I have developed the code below to solve two PDEs; first mu[x,y] is solved for, then the results of mu are used to solve for phi[x,y]. The code works and converges on a solution as is, however, I ...
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### How to solve the wave velocity in steel

In the simulation of stress wave propagation, I have the following two problems. First question: This question comes from page 69 of this book. The Lame equation for a linear elastic body without ...
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### Mesh Generation help

I am having trouble generating a mesh of a rectangle inside another rectangle. I have been following the steps on this article: https://reference.wolfram.com/language/PDEModels/tutorial/HeatTransfer/...
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### Using NIntegrate with interpolating function

I am relatively new to Mathematica and have been trying to use the NDEigensystem command to work with some quantum systems. This is actually inline with a previous question I had asked about a week ...