# 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: 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 ...
1 vote
38 views

### Neumann Boundary Condition for thermal radiation between two bodies

I'm trying to formulate and solve a pde which models thermal radiation between two bodies using a Neumann boundary condition. I've created a mesh and want to capture the thermal radiation heat ...
79 views

### NDEigensystem returns reversed list of eigenfuctions

I'm considering the two coupled linear differential operators ...
136 views

### NeumannValue is producing incorrect results

Cross-posted in Wolfram community, an online Mathematica notebook is available there. The problem under investigation is solving the Laplacian equation to model seepage. See the image below for the ...
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### Speeding up Boussinesq equations solving?

I am working on Boussinesq equation. The notebook can run perfectly for only 0.6 steps and then the calculation starts running slowly after 0.7. All boundary conditions seemed fine. I am unsure if I ...
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### Convert boundary condition involving derivative to NeumannValue programmatically

As discussed in e.g. what causes the error "The dependent variable in the boundary condition needs to be linear" when using NDSolve? When FiniteElement ...
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### How to solve 2D eigenvalue problem with robin boundary conditions

I need to solve an eigenvalue problem in 2D as seen in the picture. I've tried the function NDEigensystem but reading its documentation it seems it has issues with ...
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789 views

### How can I generate a Swiss-Cheese type region and render it transparent?

I am trying to visualize a percolation model that is equivalent to a swiss-cheese where the holes are conducting. At some point, the size of the holes gets large enough for them to touch and a ...
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75 views

### Understanding NeumannValue

From this interesting question Reveal the formal PDE of FiniteElement ...
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224 views

### Neumann boundary conditions are not satisfied

I am solving a system of 3 ODEs and I want to implement neumann BC (d/dx = 0 @x=0). However, the solution does not seem to obey neumann BC when parameter A1/A2/A3 is non zero, as I notice that the ...
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319 views

### Reproducing figure from paper on hydrodynamics

I am trying to solve Eqn. on Page 674 of https://www.nature.com/articles/nphys3667.pdf I shall quote the relevant paragraph : Next, we proceed to analyse the nonlocal response in a strip with ...
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1 vote
55 views

### Documentation of NDSolveFEMFEMNintegrate

Where can I find detailed information concerning the "NDSolveFEM" package? Thanks!
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115 views

### Using Neumann boundary conditions for the wave equation

I have the following code to solve the wave equation in 2D: ...
155 views

### Why is regioncentroid not giving correct results?

I am trying to calculate and plot the x-axis of a volume centroid for the region between zx-plane and a function squared $u(t,x,z)$ from time $t=15$ to $25$. The function is a numerical solution to a ...
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81 views

### How to stop simulation after a given model variable achieves certain value?

I would like to stop my simulation after a given model variable (say, plastic strain averaged over entire domain) achieves a given threshold value. Do you know how to do it? I'm supplying the MWE. How ...
52 views

### Why does NDSolveValue give such different answers depending on the "Method" used and without indicating an error? [duplicate]

The first two inputs below only differ in the "Method" used in NDSolveValue for the solution of the heat equation in a composite yet they give no error (the error about BCs and ICs is ...
63 views

### If or Piecewise dependent coefficients in NDSolveValue

This: but the following (placing the partials inside the If) does not. Any suggestions?
135 views

### Solving system of nonlinear PDEs

My aim is to solve a system of nonlinear PDEs arising in nonlinear elasticity. I am new to Mathematica so I started by modifying this example. I tried to change it to neo-Hookean solid. The resulting ...
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325 views

### How to generate a mesh in an area with curves inside

I would like to know how to generate a mesh inside an area, and be able to find the original curve outline inside the area from the mesh. For example: There is a rectangle inside which there is a ...
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112 views

### Simulating a gaussian pulse for the wave equation

In the process of investigating diffraction of waves, I am starting with a simple problem consisting in injecting a gaussian pulse at the boundary x=0 of a square domain and then solving the wave ...
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204 views

### Solving 2D Landau-Khalatnikov equation & Poisson equation using finite element approach

I would like to solve Landau-Khalatnikov (LK) equation and Poisson equation using finite element approach to simulate ferroelectric hysteresis loop, electric potential distribution and electric ...
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212 views

### Quarter a given triangular meshregion

For a given , examplary simple, triangular meshregion ...
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128 views

### How to do boolean operations between a large amount of regions

I want to do boolean operations between a large amount of regions. For convenience, I consider a simplified problem. The problem is as follows, digging out a large number of small hemispheres on the ...
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### NDSolve fails while solving PDE with Dancwerts BC

The following code runs with BC1 (Dirichlet Type). However, it fails for Dancwerts type BC1. ...
91 views

### Why does SolidMechanicsStrain calculated inside a module give strange results?

I am exploring the FE capabilities of Mathematica and trying a few solid mechanics problems with the aim of bringing them into my teaching. The problem is a simplified version of the coupled heat ...
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213 views

1 vote
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### Why do I see Part::partw error when using NDSolveValue?

I am using Mathematica 12.0. The present calculation is a simple "test case" to prove efficacy, but I am receiving an error I haven't seen before. e.g: ...
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198 views

### Smooth refinement for a merged 2D mesh

Thanks to @user21 response and FEMAddOns I have been able to create a multi-region mesh. I am trying to make a smooth transitional mesh refinement with respect to a ...
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1 vote
28 views

### FEM: Parsing error for ∂ in NDSolveValue? NDSolveValue: No derivatives of dependent variables [duplicate]

I came across an error/inconsistency when using inactive operators in NDSolveValue, which could be a parsing error as well as ...
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