# Questions tagged [finite-element-method]

Usage of the Finite Element Method embedded in NDSolve and details on the implementation of the fem in mathematica.

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### Combining 3D-text (extruded 2D-font) and a simple solid: RegionProduct produces invalid BoundaryMeshRegion

Below is a code fragment demonstrating a problem that has been vexing me for days. The history is in my question #298513 (thanks again to @cvgmt and @user21), but knowledge of that question or its ...
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### NeumannValue when differential equation does not use Laplacian

The context: I am attempting to solve the differential equation d^2f(x,y)/dx^2=y^2*f(x,y) on the rectangle given by (x_min,x_max)=(0,1), (y_min,y_max)=(0,1) with the boundary conditions f(x_max,y)=1 ...
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### Extrude font into a prism: BoundaryDiscretizeGraphics and Line fail to produce a RegionProduct

I am attempting to use a text character as the base of a three-dimensional prism: ...
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### Inner working of NDEigensystem [duplicate]

What is the inner workings of the NDEigensystem? How does it solve a second-order differential equation? I know it is an inbuilt Mathematica function. I want to ...
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### NDSolveValue is unable to provide a solution because of boundary conditions

I have the following Mathematica code for solving a partial differential equation, which I took from this paper (page 6, 10) for B = 0 (which has ...
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### Navier Stokes example not running

This may be a pretty noob question, but for some reason, I can't get the following Navier-Stokes FEM example to run https://www.wolfram.com/language/12/nonlinear-finite-elements/transient-navier-...
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### Cavity resonator modeling with Wolfram Mathematica

I am attempting to determine eigenfrequencies and the corresponding electric field distribution in a rectangular cavity resonator with perfectly conducting walls. In the simplest case of a rectangular ...
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### NDEigensystem does not work when using nonlinear operator [closed]

I am trying to find the eigenvalues of the stationary Gross Pitaevskii equation using the NDEigensystem command via ...
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### How to set up "mixed" boundary conditions for NDSolve for PDE? [closed]

I have the following PDE that I am able to solve using DirichletCondition with NDSolve as the following: ...
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### Solving a nonlinear PDE on a mesh with a variable density

I would like to solve the following partial differential equation in 2D on a disk with the radius 10 and centered in the coordinates origin: ...
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### Unexpected result for Poisson problem on torus (using PeriodicBoundaryCondition)

I want to solve the Laplace problem $-\Delta u=f$ ("analyst's Laplacian") for a given $f$ and unknown $u$ on the torus $[0,2\pi]/\sim$, i.e. a rectangle with opposite sides identified. The ...
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### What is resistivity function of a 3-bar electric switch?

I answered a question on Physics StackExchange - considered as homework - numerically. The question is: What is the resistance of three stacked identical blocks, the middle bar shifted by its half ...
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### How to improve FDM solver for unsteady viscous flow?

To solve the problem that is discussed in the paper Finite Difference Analysis of Time-Dependent Viscous Nanofluid Flow Between Parallel Plates we developed FDM solver based on the code from the blog ...
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### LinearSolve problem occurs as solving PDEs with NDSolve

I am new to Mathematica, please forgive me asking naive questions. I tried to solve PDEs numerically using NDSolve, but failed to go through due to errors. Two of three PDEs are time-dependent and ...
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### Dirac equation for a Coulomb potential in 2D with NDEigensystem

I want to numerically solve the ground state wave function of the hydrogen atom with the Coulomb potential using the NDEigensystem. Here is the code to get the ground state wave function from the ...
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### How to enforce DOFs to have the same values in AceFEM?

I want to make simulation of shearing of one cubic finite element as in the code below. How can I constrain all horizontal displacements (in X direction) of nodes "X"==L to have the same ...
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### Generate the full mesh of the room model

I want to import a 3d model to create a complete mesh of an interior model. ...
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### NDSolve ignores my NeumannValue boundary conditions

I am trying to solve a simple linear differential equation for $f(x,y)$ on a square with area $L\times L =1$. I consider $(\partial_x^2 + \partial_y^2)f + \partial_x \partial_y f = 0$ with the ...
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### Numerically solving radial Schrödinger equation with Yukawa potential

I am trying to solve the radial Schrödinger equation using NDEigensystem but I am running into some issues. There are posts about doing this (see here for example), ...
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### Numerical solution of the Richards' equation

I am trying to solve Richards' equation to model fluid flow in soil. The governing partial differential equation, initial condition, and boundary conditions are: The analytical solution of the ...
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### Simulating buckling

We are trying to implement buckling using a newly implemented FEM solver. However, if we try to reproduce the buckling phenomena using a thin rod, it is just compressed, and we cannot observe the ...
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### Which approximation functions does NDSolve take when solving second order ODE with the finite element method? Are they linear in parts or some other?

This is the code that I have ...
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### Post Processing of Solution and Plot of Coupled Partial Differential Equation Over a Semi-Circular Domain

Linked Question: Solution and Plot of Coupled Partial Differential Equation Over a Semi-Circular Domain.II Many many thanks to @Nasser (https://mathematica.stackexchange.com/users/70/nasser) for his ...
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### Solution and Plot of Coupled Partial Differential Equation Over a Semi-Circular Domain.II

This question is connected with reference to my previous question (Solution of Dimensionless Partial Differential Equation Over a Semi-Circular Domain), where I asked for a help to solve the following ...
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### NDSolveValue result contradicts initial condition

I'm trying to solve the Schroedinger equation in a box with two holes defined by: ...
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