# 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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### Dynamic Euler–Bernoulli beam equation

I am trying to solve for the vibration of a Euler–Bernoulli beam. The equation is $\frac{\partial ^2u(t,x)}{\partial t^2}+\frac{\partial ^4u(t,x)}{\partial x^4}=0$ For the boundary conditions I ...
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### What's inside InterpolatingFunction[{{1., 4.}}, <>]?

I'm curious what's inside the InterpolationFunction object? For example: ...
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### Least effort to handle a point source inside the domain of PDE(s)

By point source I mean a constrained condition at one point inside the domain of PDE(s). For example: \frac{\partial ^2u(t,x,y)}{\partial t^2}=\frac{\partial ^2u(t,x,y)}{\partial x^2}+\frac{\...
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### How to apply different equations to different parts of a geometry in PDE?

I want to solve two coupled partial differential equations on two dimension. There are two variables v and m. The geometry is a ...
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### Solving Stefan's solidification problem - for the case of 3 regions

This question heavily related to this question, where the case of two PDE's are solved along with a zipping condition that is a function of time. Using the link in the code I have solved this set of ...
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### Is it possible to re-mesh, downsample & upsample a DiscretizeRegion object?

In my project, I am importing a complex geometry from an STL file into Mathematica as a MeshRegion. I would like to edit this mesh significantly: For instance, drastically reduce or increase the ...
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### Solve Laplace equation in Cylindrical - Polar Coordinates

Hey mathematica stackexchange!! I've got a (possibly stupid) problem. I've tried many things to no avail, and I've read every post I've found on Laplace's equation. Background: I'm trying to find the ...
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### Controlling dynamic time step size in NDSolveValue

Statement of problem I'm writing a script to calculate the temperature of a 2D system with time-dependent heat deposition. The heat deposition is a square wave pulse of duration w = 10^-6 seconds, ...
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### NDSolve with equation system with unknown functions defined on different domains

Based on @xzczd's excellent answer on solving an equation system with unknown functions defined on different domains, I've tried to apply the same technique to a similar system shown below: Equations: ...
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### Incorrect results of diffusion equation with Neumann boundary conditions [duplicate]

I want to resolve a PDE model, which is 1D heat diffusion equation with Neumann boundary conditions. The key problem is that I have some trouble in solving the equation numerically. Consider the ...
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### Creating a 2D meshing algorithm in Mathematica

As what is proving to be a difficult, but entertaining task, I am attempting to adapt a 2D meshing algorithm created for MATLAB and port it to Mathematica. I understand meshing functions already exist ...
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### Calculating a potential function using the finite element method

This is my first attempt to use the Finite Element method available in version 10. There are questions and I am very open to suggestions. My example is flow around a cylinder which is a well known ...
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### Optimizing a Numerical Laplace Equation Solver

Laplace's Equation is an equation on a scalar in which, given the value of the scalar on the boundaries (the boundary conditions), one can determine the value of the scalar at any point in the region ...
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### Poisson equation with pure Neumann boundary conditions

Dear Mathematica users, I would like to numerically solve a, as the title says, Poisson equation with pure Neumann boundary conditions $-\nabla^2(\psi)=f$ $\nabla(\psi)\cdot \text{n}=g$ Is it ...
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### Numerically solving an inhomogeneous partial differential equation

I'm trying to solve a cylindrical partial differential equation with boundary conditions. But I got an error message saying ...
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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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### Why should the spatial derivative order of the ODE *not* exceed two?

Following this question I came across this strange behaviour. Let me define a 1 D interval implicitely ...
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### NDEigensystem for structural vibration

Having installed version 11 I thought I would check an old Stack Exchange vibration problem using NDEigensytem. The old problem was Test a wooden board's vibration mode and I think this was before ...
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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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### what causes the error "The dependent variable in the boundary condition needs to be linear" when using NDSolve?

V 12.1.1 on windows 10 Why the following works ...
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