# 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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### Interpolation Failing on Data of a Certain Size

I'm trying to interpolate the following unstructured data set so I can compute and plot the gradient. ...
49 views

I am trying to solve a nonlinear PDE - 1D diffusive heat equation. I'm not sure what is wrong (am new to Mathematica). I'm trying to use https://reference.wolfram.com/language/FEMDocumentation/...
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### Area of an Annulus (MeshTools<>NIntegrate)

In a very simple example I try to describe an annulus using MeshTools package mesh2D = AnnulusMesh[{0, 0}, { 1 , 2 }, {-Pi, Pi}, {36, 10}]; The area given ...
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### Creating single AceGen element using the same constitutive model defined for 2 fibre families

I'm currently working with a single constitutive model that describes 2 collagen fibre families that have different element properties. The strain energy density function is W, where there would be 2 ...
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### Non-Newtonian Momentum Eqn in a rectangular pipe

I am trying to (numerically) solve the momentum eqn for a non-Newtonian fluid in a pipe with rectangular cross section using Mathematica. Here are the assumptions: So, the flow is only in z ...
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### Error when trying to solve elastic PDEs using FEM: “Compile::argcompten: The comparison, LessEqual, is invalid for tensor arguments.”

I'm trying to solve the following linear elastic problem: The pairs of numbers beside each node is the coordinates in meters. The loads are in Newtons. The part of codes that probably have no ...
188 views

### Transient Heatflow in a Wheel Disc Brake

I try to model the Convection–diffusion equation for a rotating 3D annulus(small thickness): The temperature u[t,x,y,z] is described in cartesian coordinates. ...
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### Heat Flow in a Pipe

I try to model the transient heat flow in a pipe, assuming that the temperature in radial direction doesn't change: temperature ...
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### Electrostatics: Finite Elements

I'm messing around with FEM in mathematica and am having trouble solving a very simple problem of the electric field around a unifromly charged sphere. Here is my workflow. ...
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### NIntegrate over regions, FiniteElement options

I am using NIntegrate to integrate a 3-dimensional region. When I don't set any integration options, I get a warning The global error of the strategy GlobalAdaptive has increased more than 2000 ...
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### 1DPoisson equation with Dirac delta

I was writing my own FEM method to solve the Poisson equation \begin{align} -u'' &= \exp(-c(x-1/2)^2)\\ u(0) &= u(1) = 0 \end{align} where c=100. and I'm reading from the book of Mats G. ...
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### Generating Mesh of Rotated Graphics

I have a simple geometry that consists of a few rotated rectangles ...
126 views

### Error trying to solve a 2D elasticity problem using FEM package

I have the following equations $$\frac{\partial{N_x}}{\partial{x}}+\frac{\partial{N_{xy}}}{\partial{y}}=0$$ $$\frac{\partial{N_y}}{\partial{y}}+\frac{\partial{N_{xy}}}{\partial{x}}=0$$ where \begin{...
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### Laplace equation DirichletCondition ignored

My goal is to find out force between two parallel identical disks with Voltage difference. To solve this, I tried to use laplace equation. And below is my code. where R is radius of disks, d is ...
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### How to mesh a region with inclusions touching the boundary

Suppose you have a region composed of two materials. You define the inclusions of material 1 through, e.g., disks, ellipsoids, ...
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### Unexpected error when implementing FEM in MoL SpatialDiscretization

I cannot figure out why the following piece of code ...
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### Problems with Neumann (zero flux) boundary conditions

I have the following code: ...
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### Why does domain size change results of NDSolve? / How to overcome this?

this is a follow-up on a previous question which was answered, but it turned out that I was running in circles... I have the following code: ...
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### Thermal conduction (Annulus, 2D): Missing boundary conditions

The thermal conduction problem, described in polarcoordinates can be solved ...
82 views

### Unable to use ElementMarker in DirichletCondition with structured quad mesh

I would like to use ElementMarker in a DirichletCondition on a structured quad mesh, but I am receiving the error: ...
92 views

### Solving system of PDEs with NDSolve

I am trying to solve a system of coupled PDEs with zero-flux boundary conditions on a large domain. I have two problems: 1) Is there a possibility to use results of NDSolve as inititial conditions? ...
151 views

### One dimensional heat exchange on a ring: Periodic solution

Subsequent I consider the transient heat exchange problem of a ring in polar coordinates. The ring is heated in a small range 0<\[CurlyPhi]<20° and cooled ...