# 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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### From where to learn finite element method?

Can anyone reccomend me a book or site for learning finite element method with mathematica, besides wolfram language official site, https://reference.wolfram.com/language/FEMDocumentation/tutorial/...
353 views

### Create vtk file of ParaView from Mathematica [FEM post-processing]

I'm doing FEM in Mathematica and want to visualize the results in Paraview (e.g., create a video of the displacement field). Now I have the element mesh, the displacement and stress fields. How can I ...
508 views

### Stress Operators for Finite Element Analysis

For stress analysis in the finite element method you need a stress operator. For two dimensional plane stress it can be found here. For two dimensional plain strain it can be found here. I need the ...
564 views

### benchmark of Mathematica's FEM?

Does anyone have any numbers on how mathematica compares to other commercial (eg ANSYS) or free FEM softwares (eg. FreeFEM++, FEniCS, elmer)? If this is too vague say solving the diffusion equation in ...
468 views

### FEM Mesh for pipes and tubes

I work with pipe systems and would like to use finite elements within NDSolve for regions inside or exterior to a pipe. How to do I make a mesh of the region ...
516 views

### Symbolic Weak Form

Usually I write the weak form by hand for my FEM code, but it's a little annoying and mechanic sometimes. So, I wonder, is there any way to generate the symbolic weak form in Mathematica? For ...
355 views

### How to increase boundary mesh quality?

Update: I tracked down the current issue to errors generated by numerically integrating over the boundary mesh. What's the proper way to integrate a function over the boundary of an implicit region? ...
153 views

### Transition to turbulence

I found that a 3D model of viscous flow in a rectangular channel with jump section implemented on the basis of FEM demonstrates a transition to turbulence. We use an algorithm for unsteady flows ...
172 views

### NDSolve post-processing: Calculate the flow over a FEM-boundary

I'm trying to calculate the heat loss from buried pipes with NDSolve`FEM. For this I set Dirichlet conditions at the model top and bottom and temperature dependant Neumann conditions at the contact ...
72 views

### system of coupled nonlinear pdes with FEM (magneto-hydrodynamic mass transfer)

EDIT 01 See end of post for an update. Original Question I'm trying to reproduce the magneto-hydrodynamic flow studied here using the nonlinear FEM functionality, and have been having trouble ...
205 views

### Problem computing a cylindrical Heat equation with a parameter alpha

i have been struggling to compute a particular instance of cylindrical 3D heat equation. Here is my code : ...
55 views

For long tutorials, I prefer hard copy. Is it possible to download from somewhere this document https://reference.wolfram.com/language/FEMDocumentation/tutorial/FiniteElementOverview.html as PDF ...
85 views

### 1-D stress (displacement) analysis in annulus by considering viscoelasticity

I am a new Mathematica user, and I was trying to solve a stress (or displacement) field problem in an annulus. Here is the problem in the polar coordinate: The inner radius of the annulus is $b$, ...
62 views

### Interface points of NDEigensystem

When solving an eigenvalue problem with "NDEigensystem", e.g. a 1D Eigenvalue problem with the interval composed of different materials, which should be solved by the pure numerical method such as FEM,...
170 views

### Postprocessing of FEM: extremely slow speed of NIntegrate

I've gone through the documentation for NDSolve FEM. There are quite a lot tips and techniques for accelerating NDSolve, and only quite few tips for post processing. Somehow I found out that the ...
168 views

### Using of FindMinimum in constrained problem

There is a constrained optimization problem based on finite element method. We should find the optimal distribution of density inside the our region for minimazing the energy of deformation. The ...
242 views

### Reducing a FEM 3D Interpolation Function to a 2D Interpolation Function

I'm trying to solve the heat equation in 3D using FEM and back out a slice in the xz plane. My problem is when I define a function that is a slice in the xz plane it uses the full 3D interpolation ...
133 views

### Stress analysis in a disk with circular holes

Writing the following code: ...
162 views

### Coupled parabolic differential equations with time delay

Is it possible for NDSolve to solve delay partial differential equations with simple Neumann boundary conditions? An example I have is as below: ...
1k views

### FDTD Electromagnetic Simulations with Mathematica

Mathematica has some Finite Element capabilities (as explained here). Do you think mathematica is a realistic/sensible option for electromagnetic simulations? (aka making a movie of electric fields ...
276 views

### How can I improve the solution of my PDE?

I want to improve the last code to find a better solution for umi. For now I'm using only MaxStepFraction. Also, when I put no ...
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### How to Implement a “Function Object” suitable for NDSolve and Finite Element Method?

I have a bunch of methods that shoud return an expression that behave like a function, i.e. an expression that, when supplied with suitable arguments, evaluate to something. A simple ...
233 views

### Puzzling NDSolve[] behavior for PDE (smooth solution, inconsistent with boundary conditions)

Consider the following: NDSolve[{D[z[x, y], x, x] + D[z[x, y], y, y] == 0, z[x, 0] == Sin[x], z[0, y] == Cos[y]}, z[x, y], x, y] {{z[x, y] -> ...
58 views

### How to numerically integrate the time of two oscillatory functions from NDEigensystem

I am trying to numerically integrate phi*psi. And no matter which method I chose, the NIntegrate failed. ...
71 views

### NDSolveValue not working correctly

So I am trying to get a good representation of the 2d heat equation with mathematica but it does not seem to work correctly: ...
90 views

### Why is there no heat being transfered in my program?

I have been working on this code and am new to this coding language. I have been trying to model the transfer of heat through a hot plastic being cooled in a water bath. For some reason I have not ...
88 views

### Heat transfer FEM with nonlinear Cp

I would like to solve a 3D heat transfer problem with nonlinear heat capacity Cp (Cp=1*T[t,x,y,z]). My problem is very simple: a slab with the bottom surface insulated and the other five surfaces ...