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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3
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1answer
253 views

2D Oseen equations

Background info: https://en.wikipedia.org/wiki/Oseen_equations ...
0
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1answer
38 views

Can I convert my SMTShowMesh Object into a mathematica graphics object in AceFem?

My question is related to a string of questions Ive asked in the last few days. I'm trying to superimpose a vectorplot on a3D plot that I've produced on AceFem using the SMTShowMesh Command. I'm ...
5
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1answer
145 views

NDSolve::femcmsd: The spatial derivative order of the PDE may not exceed two

I was in the impression that V12 can now handle higher order PDES but for this particular case it fails to produce any solution. ...
2
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1answer
75 views

Plotting fibre direction at each node

I was wondering if there was a way to plot the direction vector of a fibre family at each node in AceGen/AceFem? Below is an example of exactly what I want to do but I do not know how to recreate it. ...
5
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1answer
86 views

FEM: does the term $\gamma$ in “The Coefficient Form of Partial Differential Equations” has to be an explicit list?

In the FEM documentation, "The Coefficient Form of Partial Differential Equations" is I am interested in its simplification to $$ \nabla \cdot (-c \nabla u + \gamma) = 0 $$ where $c$ should be a ...
3
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1answer
121 views

Solution of convection dominated PDE with conditions only on the interior of the domain

I'm Trying to solve the following PDE: $$ \frac{1}{20}\left(2 x_1^2+x_2^2\right) -25\left( \begin{bmatrix} 0\\ \frac{6 \cos(x_1)}{-37 + 3 \cos(2 x_1)} \end{bmatrix}^\intercal \nabla_{x_1,x_2}V(x_1,...
4
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2answers
178 views

FEM: Solving the heat conduction with 2D periodic condition

Suppose you have a region $\Omega = [0,P_1] \times [0,P_2]$ which is composed of, e.g., two materials. One material is distributed as inclusions in an embedding material. We split the region as $\...
8
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1answer
201 views

Nonlinear elasticity PDE in Mathematica 12

Mathematica 12, Windows 10. I am trying to solve a PDE in one spatial dimension $R$ and time $t$. I need a solution for displacement $r(R,t)$, radial Cauchy stress $T_{RR}(R,t)$, and radial growth $\...
6
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1answer
79 views

How to help NDSolveValue handle the addition of another dependent variable in a set of reaction-diffusion equations

I am trying to use NDSolveValue to solve a system of coupled reaction-diffusion equations in a 2D space (technically 3D cylindrical coordinates, but due to radial ...
3
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1answer
62 views

NDSolve Stiffness and Strange Behaviour with Dirichlet Conditions

I working with the following semiconductor potential equilibrium equation for a diode $$\psi(x)''=e^{\psi(x)}-e^{-\psi(x)}+10^6\text{sgn}(x-(l+r)/2)$$ where $l$ and $r$ are left and right boundaries ...
7
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2answers
117 views

Using mesh cell highlighting to override the default rendering of a region

The default rendering of a region can be rather uninformative. Consider this simple example. DiscretizeRegion[Rectangle[{0, 0}, {2, 1}], MaxCellMeasure -> 2] ...
3
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1answer
59 views

About the accuracy of Method -> FiniteElement in NDSolve, version 12.0

In this question, the equation $uu'=\nu u''$, $x\in (-1,1)$, $u(-1)=1+\delta$, $u(1)=-1$, was considered. The question asked about how to solve this differential equation problem in Mathematica. There ...
2
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1answer
112 views

Issues with NDSolve when solving a system of two coupled PDEs

I'm trying to solve a system of non-linear reaction-diffusion-advection PDEs numerically using NDSolve. The two equations are (taken from here): where $H(x)$ is ...
2
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1answer
264 views

Global Stiffness Matrix Assembly [closed]

I am trying to assemble the global stiffness matrix and global force vector from the local stiffness matrix and local force vector using a function Forcestiffness Assembly as follows: where FA[no ...
2
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0answers
60 views

NDSolve Error “message text not found” [closed]

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/...
6
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1answer
147 views

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 ...
1
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1answer
38 views

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 ...
2
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3answers
216 views

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 ...
1
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0answers
58 views

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 ...
8
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1answer
211 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. ...
6
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3answers
243 views

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 ...
4
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2answers
211 views

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. ...
1
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1answer
95 views

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 ...
8
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2answers
148 views

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. ...
10
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2answers
316 views

Generating Mesh of Rotated Graphics

I have a simple geometry that consists of a few rotated rectangles ...
6
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2answers
153 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{...
5
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1answer
99 views

Eigenvalues and numerical eigenfunctions for similar differential operators

I am looking to numerically approximate the eigenvalues and eigenfunctions for a differential operator I am working with, assuming $\pi$ periodic boundary conditions. Namely, I define the function $...
4
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1answer
173 views

Poor convergence for first order PDE using FEM (Laplace's equation in a disk)

Consider Laplace's eqn in the unit disk, r^2 D[u[r, t], {r, 2}] + r D[u[r, t], {r, 1}] + D[u[r, t], {t, 2}] == 0. The general analytic solution is easy to work out,...
3
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2answers
251 views

Solve a one dimensional heat transfer problem with NDSolve

The following problem is a 1-D heat transfer conduction problem: where, I am trying to solve with NDSolve like this way: ...
7
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1answer
221 views

Curved Dirichlet boundary in FEM

Based on this fascinating blog post (https://blog.wolfram.com/2013/07/09/using-mathematica-to-simulate-and-visualize-fluid-flow-in-a-box/) from a few years ago that shows how to simulate a driven ...
1
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0answers
64 views

internal Neumann boundary for FEM

Following the documentation for NeumannValue (https://reference.wolfram.com/language/ref/NeumannValue.html) gives the impression, that it is only possible to set ...
7
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2answers
262 views

Solving a steady-state viscous Burger's equation with NDSolve

A steady-state viscous Burger's equation is given by $$ u\,u'=\nu \,u'', \quad x\in (-1,1), $$ $$ u(-1)=1+\delta,\quad u(1)=-1.$$ Here $\nu>0$ is the viscosity, $\delta>0$ is a small ...
2
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0answers
51 views

Is Inactive Form avoidable when using NDSolve for non-linear ODEs

So this is basically the same question as here referring to information provided here. However, I am wondering if this inactive form is always necessary or more of a convenience. For example, ...
1
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1answer
145 views

Numerical problems when solving a 2-dimensional Fokker-Planck equation

I try to solve a Fokker-Planck equation fpe = D[p[x, y, t], t] + Div[j, {x, y}] == 0; with ...
2
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1answer
191 views

Heat transport in 1d, two different materials at point contact with NDsolve -

I have two materials touching at a point x=0. 1) The first material lies within the interval [-L1, 0], has diffusion constant D1, and the heat conductivity kappa1. Its left end is kept on time ...
3
votes
1answer
122 views

How to use only Neumann boundary conditions and a normalization constraint on a PDE

I'm trying to solve the stationary PDE c = {{5, 0}, {0, 5}}; alpha = {x - 50, y - 50}; pde = Div[-c.Grad[u[x, y], {x, y}] - alpha*u[x, y], {x, y}]; (following ...
4
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1answer
215 views

Electric field produced by a capacitor consisting of two parallel plates of different lengths

I need to visualize the electrostatic field produced by a capacitor consisting of two parallel 1D plates of different lengths, as shown in the following figure (sorry for the crude drawing), in which ...
0
votes
1answer
142 views

How to solve transient 3D heat equation with robin boundary conditions

Good afternoon! I'm trying to solve the following heat equation: with the following boundary conditions and initial value: Nut I'm getting error while solving it with NDSolve: ...
3
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1answer
82 views

Finding eigenvalues of the Laplacian on solenoidal (divergence-free) vector fields

In Mathematica it is easy to find eigenvalues of the Laplacian in simple cases. For example, on $\Omega\in \mathbb{R}^2$: ...
4
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1answer
201 views

Solving the Stokes equation for planar Marangoni flow with FEM

Background I would like to numerically solve the stationary Stokes equation from fluid dynamics $\eta_i \nabla^2 \vec{u}_i - \nabla p = 0$ with the incompressibility condition $\nabla \cdot \vec{u}...
3
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1answer
95 views

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 ...
8
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2answers
164 views

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, ...
2
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2answers
125 views

Finding eigenvectors of a differential operator

How can I find the eigenvalues and eigenvectors(numerically) of the below matrix equation: $ \qquad \hat{A}\left({\begin{array}{c} y_1(x,\theta)\\ y_2(x,\theta) \\ \end{array} } \right)= ...
9
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2answers
223 views

The FEMDampingElements operator failed

I am using Mathematica's (v12.0) NDSolveValue method to solve a finite element method problem (Navier-Stokes equations for a compressible gas). During the initialization process at t==0, I repeatedly ...
4
votes
2answers
216 views

NDSolve::ntdvdae: Cannot solve to find an explicit formula for the derivatives

I am facing these error messages, NDSolve::ntdvdae: Cannot solve to find an explicit formula for the derivatives. NDSolve will try solving the system as differential-algebraic equations. plus ...
4
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1answer
121 views

Adaptive Meshrefinement NDSolve&FiniteElements

In a simple example I try to solve the heat equation using NDSolve and Method->"FiniteElement". I know that NDSolve gives ...
3
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2answers
74 views

Checking NDEigensystem Results

I'm looking to verify the output of a call to NDEigensystem. I'm doing this by plotting the operator acting on the Interpolating Function outputs versus the ...
3
votes
1answer
89 views

Coupling DirichletCondition of one dependent variable to the value of the second

Maybe due to my limited experience with PDEs solving I could not find the answer to the following issue. Let's say we have a simple advection along a line: ...
0
votes
1answer
85 views

Nonatomic expression expected at position 1 in First[None]

This is a follow-up question to an earlier question:Solving a system of PDEs on a piecewise polynomial domain. I tried to solve the system of equations from one of my previous post with the different ...
6
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3answers
471 views

Compare FEM mesh with the mesh created within Mathematica

This is a follow-up question to an earlier question: Make uniform mesh with quad elements Question: How to solve system of equations with NDsolve on the mesh created in Ansys in order to compare it ...

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