# 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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### FEM: periodic solution of 2D Navier-Stokes equations

Let’s consider a horizontal channel with a round obstacle in the middle. ...
78 views

### why on some MaxCellMeasure values, FEM gives internal 1/0 error?

V 12.1 on windows 10 When I was answering NDSolveValue taking too long I noticed the following When I use some value for MaxCellMeasure, then FEM gives 1/0. Why ...
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### NDSolveValue taking too long

I am trying to solve heat diffusion equation on hollow cylinder with constant DirichletCondition on inner radius and zero ...
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### To obtain eigenvalues and eigenvectors from FEM solution

I have a model which solve a 2D coupled elasticity problem. Now I'm trying to get the eigenvalues and eigenvector from that solution. But, following the very first step to get stiffness and load ...
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### How to Improve FEM Solution with NDSolve?

First some comments. This same calculation works beautifully in 2D with essentially the same code. I have copied it largely unaltered into 3D as part of a migration to 3D so that I can do more complex ...
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### How to learn numerical solving PDEs in WM?

I started to try to solve PDEs in WM and I go gradually according to tutorial. Unfortunately, I couldn't get any solution other than that copied from the tutorial. So I ask someone more experienced to ...
120 views

### Wall boundary condition in inviscid flows with NDSolve

I am trying to duplicate https://www.wolfram.com/language/12/nonlinear-finite-elements/navier-stokes-equation.html?product=language Naiver-Stokes type simulation for a charge current density. If I ...
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### Quasi-periodic boundary conditions

I am trying to solve the following problem using Mathematica's NDSolve $$\partial^2_{y}\psi+\partial^2_{x}\psi-2\,i\,q\,B\,y\,\partial_{y}\psi-q^2B^2y^2\psi+q\,B\,\psi=0$$ subject to the boundary ...
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### Trying to use output of ParametricNDSolve as Dirichlet conditions for another ParametricNDSolve

My apologies if the problem was already solved in a similar thread, but i was not able to find a working answer. I am trying to numerically solve a quite cumbersome PDE of second order which requires ...
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### RegionUnion Fails for Overlapping 3D Regions

Bug introduced in 12.0 or earlier and persisting through 12.1.0 Warning: The below code may crash your kernel! I am trying to make a (simple) 3D mesh of a box for a FEM solution (I am using MMA 12.1 ...
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### Is WM able to solve PDEs (non-linear with variable coefficients) with variable initial conditions?

I'm learning how to solve PDE from tutorial. My question is about passage: "The transient Navier–Stokes equation" (code below) at the end of tutorial. First, there is a stable flow through the ...
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### High peaks of FEM solution

Following this question and user21 answered, I changed the BCs of the initial problem. The code following bellow. ...
64 views

### System of PDEs with delay, MapThread error

I have the following code: ...
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### Assigning ElementMarkers to existing ElementMesh boundaries

I've imported a 2D element mesh from another program as a list of triangle coordinates {{x1,y1},{x2,y2}....} ("nodes") and element connections {{n1,n2,n3},...} ("elements"). Then I create an ...
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### Overflow with NDSolve

Backslide introduced in 10.0, persisting through 12.1. I am trying to solve the following differential equation and plot the result: ...
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### Problem with a solution of PDE with initial and boundary conditions

I would like to solve relativistic hydrodynamic equations (nonlinear PDEs) introduced here: I use eqs (33 - 35), (38 - 41), where (40) P(rho)=k*rho^g0 (all with one spatial coordinate "mu" and one ...
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### NDSolve for 2D Laplace equation with mixed boundary conditions

I used NDSolve to solve the 1D Laplace equation for phi with a Dirichlet boundary condition on the left boundary and a Neumann boundary condition on the right. The calculation for phi relies on the ...
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### Error using FEM package

I'm getting the following error: NDSolveValue: The FEMStiffnessElements operator failed. I looked for this error in FEM documentation and did not find anything. I'm using Mathematica 12. It ...
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### How to divide a region in FEM with a parametric curve?

I'm using NDSolve with finite element to try to solve a heat transfer problem. The region I have is a rectangle where the four vertices are at ...
533 views