# 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/...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### How can we improve transonic flow visualization?

With this code we can make 2D FEM simulation of transonic flow around airfoil NACA 0012 at Mach number of 0.925. It takes about 5 minutes on the XENIA-15 laptop of 32 GB memory with processor Intel ...
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### Numeric Solution Hydrogen Atom

I'm trying to solve the Schrödinger equation for the hydrogen atom without made the variable separation of the polar and radial coordinate. It is my test code to extrapolate to another system with its ...
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### Does current Mathematica capability allow solving PDEs (e.g. reaction diffusion equation) over surface of a mesh or surfaces

I came across this nice paper (https://arxiv.org/pdf/1605.01583.pdf) where the authors simulated a reaction diffusion system over the surface of a gecko, primarily to understand how various patterns ...
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### 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 ...
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### ParametricNDSolveValue causes kernel to crash

Bug introduced in 12.1.1 and persisting through 13.2.0. In the course of answering question 228693, I found that ...
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### 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 ...
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### 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? ...
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### NDSolve post-processing: Calculate the flow over a FEM-boundary

I'm trying to calculate the heat loss from buried pipes with NDSolveFEM. For this I set Dirichlet conditions at the model top and bottom and temperature dependant Neumann conditions at the contact ...
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### 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 ...
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### Inactive PDE terms in FEM without Neumann boundary conditions

I am solving a Poisson-like set of PDEs for u[x,y] and v[x,y] in the square region ...
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### Solve 3D convection-dominated PDE with discontinuous coefficient, without tiny mesh

I'm trying to simulate a self-propelled particle diffusing on a disk. The direction of the self-propelled velocity $\vec{v_A}$ doesn't change, while it speeds up at the boundary and slows down at the ...
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### FEM: modelling 2D flow under periodic forcing

Despite many examples of periodic boundary conditions being presented, it remains difficult to obtain a periodic solution. Let us consider a simple example of a flow in a two-dimensional channel under ...
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### 1st-order linear ODE system gives inaccurate/biased solutions

Consider an ODE eigensystem  t(y+\frac{1}{s})a(y)+[(q+\frac{1}{2}+\frac{s}{2}y)+s(y\partial_y+\frac{1}{2})]b(y)=\lambda a(y)\\ t(y+\frac{1}{s})b(y)+[(q+\frac{1}{2}+\frac{s}{2}y)-s(y\partial_y+\frac{...
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### Numerical instability when using NDSolve to simulate phase separation

I'm using NDSolve to simulate the following model of phase separation: where rho_T=rho_1+rho_2. The term with chi causes rho_1 and rho_2 to repel each other. However, there is a numerical instability ...
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### Implementation of Neumann-like boundary condition

If we wish to solve an elliptic PDE, say $\nabla^2\phi=\text{given}$, on a domain $\Omega$ with Neumann boundary conditions, $\hat{\mathbf{n}}\cdot \nabla \phi\Big|_{\partial \Omega}=\text{given}$, ...
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### 3D BoundaryMeshRegion Minkowski difference via RegionErosion Failure

I need to be able to produce Minkowski difference of an arbitrary BoundaryMeshRegion and a cylinder. ...
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### Make NDSolve return solution over only part of domain

Consider the following pair of PDEs, for which I will solve in the mesh built below. The mesh needs to be much larger than the region of interest to mimic boundary conditions "at infinity". ...
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### Coupled PDEs with different dimensions and boundary conditions

The geometry of the problem is described by a cylinder inside a rectangular domain. The equations describes the region in between them. I have 2 PDEs for U(x,y,z) in the bulk region and V(z) for -0.5&...
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