# 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 in 3D: assigning proper mesh for NDSolveValue

I am trying to compute electric potential in a simple 3D geometry containing (in a simplied version) 3 conductive rings (2 outer rings at 0 V, and the inner at 1 V) in different planes and I don't get ...
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### Calculating the 3D Vector field of a permanent magnet with FEM

trying to calculate the magnetic field of a permanent magnet using the finite element method I struggle setting up the equation system properly. In the end I want to be able to calculate the magnetic ...
84 views

### The heat equation on the intervall [0,1] with Robin Boundary

I have the heat equation on the invervall $[0,1]$, therefore I define heqn = D[u[x, t], t] == D[u[x, t], {x, 2}]; and I define my initial data which can be boring, ...
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### Unable to plot a solution of NDSolve whilst being able to evaluate it

I want to define a function $f_c(x,y)$ as the solution of the PDE $\Delta f_c(x,y) = g_c(x,y)$, where $g_c$ is a given function depending on a constant $c$. I tried the following: ...
262 views

### How to solve this PDE

I had a try at numerically solving the heat equation with a source term: $$\frac{{\partial x}}{{\partial t}} = D\frac{{{\partial ^2}x}}{{\partial {z^2}}} + c$$ ...
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### Using the result of NIntegrate as a potential in NDEigensysem

I am trying to find the eigenvalues and eigenstates of a Hamiltonian with a potential which cannot be analytically defined. In particular, it is the integral of the product between two functions: <...
121 views

### How to solve Coupled a Parabolic and Elliptic PDE in NDSolve?

I want to solve a mixed PDE Parabolic-Elliptic system in 3-dimension (rectangular coordinate), as shown below: The respective code version with parameters value, boundary and initial conditions is, <...
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### Coupled pde for multiphysics joule heating with temperature dependent properties - error inconsistent dimensions

I want to simulate 3D joule heating and followed the wolfram multiphysics tutorial. This multiphysics problem is comprised of the equation for the voltage field: and the heat equation: with the ...
180 views

### 3D FEM Mesh - Accessing values of individual boundary elements

I have 3D mesh and calculate the heat equation using NDSolve. I want to access the temperature values on the individual boundary elements to solve another problem (...
92 views

### FEM Mesh - how to get elements belonging to ElementMarker

I want to get a list of all boundary elements belonging to a certain ElementMarker of a boundary mesh. This code creates a simple mesh and allows to inspect the <...
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### Can Mathematica do thermal/mechanical analysis of modeled solid systems?

I want to do thermal and mechanical analysis of various parts which may have complicated geometries. I am contemplating buying SolidWorks because it does this: you model the part and then use their ...
219 views

### FEM 1D 3D region coupling - speed up coupling using boundary integration

I am working on a simulation of the heat equation involving a 3D solid simulation coupled to a 1D fluid simulation (convective term of heat equation). I am using the method of false transient as ...
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### FEM 1D 3D region coupling - integration too slow for coupling with energy conservation

EDIT: I reposted this question, removing everything that is not necessary for my coupling approach. Find the new post here. I am working on a 3D simulation of the heat equation which is coupled to a ...
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### FEM Meshrefinement for 1D Interval and Elements of order 2

I would like to create a 1D mesh of the intervall (-pi/2,pi/2) for solving a DE with FEM, with more elements close to +-1 - these elements should be of order 2, since order 1 elements yield too low ...
74 views

### 3D FEM - How to use element markers for boundary integration

I am having trouble integrating over some curved boundaries and was thinking about using the element markers of the boundary mesh for integration rather than conditionals. Is it possible to use ...
59 views

### Interaction between fluid flow and elastic obstacle (fluid-structure interaction) [closed]

I would like to model the velocity and pressure distribution of an elastic obstacle in a channel where the fluid flows. There are Navier-Stokes examples in Mathematica webpage with rigid obstacles but ...
77 views

### How to numerically solve Laplacian Equation in a system dependent boundary conditions?

I would like to solve the Laplacian equation in the following system in order to find out the potential and the Electric field everywhere. I have solved a couple of exercises by solving numerically ...
84 views

### FEM nonlinear anisotropic heat transfer with element markers

I'm trying to model a 2D nonlinear anisotropic heat transfer using FEM with element markers. I got stuck with errors and have no idea what to do to make it work... I have simple toy-model: two ...
74 views

### Fail to inverse the Piecewise function embedded in a NDSolveValue

I am trying to estimate a function consisting of a Piecewise function that included in a FEM solver. I firstly developed my mesh for the FEM model based on @Tim Laska's work. The code is shown as <...
60 views

### Obtaining more values from NDEigenvalues

When I run this code ...
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### Solving Fokker Planck Equation for steady state solution using NDSolve

I am trying to solve the FPE (Equation (4) in paper) for the steady state solution to reproduce Fig 2(b)&(c) in mathematica using ND Solve. The functions and parameter values I used are as ...
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### Custom mesh to help with a Fokker Planck eqn (refined rectangular mesh?)

Physicist here, new to SE and fairly new to MMA. I'm looking to solve a Brownian motion problem with inertia (m ≠ 0) and a velocity dependent diffusion coefficient, which in dimensionless units and ...
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### How can I solve the 2D diffusion equation over a region that contains mobile sinks?

I am looking for guidance on how to simulate the following system in 2D. I have a region, assumed to be rectangular for simplicity. A substance is diffusing into this region from its boundary. Again ...
81 views

### NDSolveValue for 2-D heat equation (PDE) coupled with ODE boundary and DiracDelta function [closed]

Recently, I am studying on the point source problem (PDE with DiracDelta) for heat equation. The equations are as follow The problems are arisen from not only the DiracDelta issues but the nonlinear ...
65 views

### Solving differential equation system with FEM when the equations depend on the mesh cell size

I am trying to implement Large eddy simulation with FEM for solving air flow simulation using Smagorinsky sub-grid stress model. In order to implement this there is a parameter (filter size) in the ...
93 views

### Define Implicit Region using Interpolating Function

Suppose I have a set of points $\{(x_1,x_2) : g(x_1,x_2) > f(x_1,x_2)\}$, how would I turn this into a mesh that acts as a region for PDE solvers, or even to use as a plotting region? I have tried ...
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### Boundary Value of Function Disagrees with Neumann Boundary Heat Equation

I'm trying to solve a time-dependent 2D heat equation with a source, initial specified heat distribution and heat flux loss at the boundary which goes with the temperature difference. Thus far, I've ...
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### NDSolve with Piecewise function consideres some value inside Piecewise as Indeterninate

I'm solving a PDE, with one coefficient being piecewise. The issue appears to be that NDSolve somehow consideres piesewise boundary as ...
52 views

### Define the heat capacity Cp as constant values in the current version of Mathematica (Coupled PDEs)

I am trying to model a 2d heat transfer in fluid flow with nonlinear heat capacity Cp (e.g. Cp=1 + T[t,x,y]). This benchmark problem is described as: the left side of the plate is heated, and the ...
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### Modified Heat Transfer in Fluid Flow

I am trying to simulate Modified Heat Transfer in Fluid Flow (based on Buoyancy-Driven Flow in a Square Cavity ). The modified heat transfer takes the form: with the solid volume fraction: The ...
193 views

### Different answer between HeatTransferPDEComponent and Matlab

I've been working on a 2-layer HeatTransferPDE Model. The diagram of the model is The two materials have an initial temperature of 37℃, and the outside is 75℃. The model is for heat insulation so it ...
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### NDEigensystem potential with a singularity

Consider the following eigenvalue equation $$-\frac{d^2}{dx^2}\Psi_n(x)+\left(gx^4+\frac{1}{x^2}\right)\Psi_n(x)=E_n\Psi_n(x),\qquad x\in(-10,10),\qquad\Psi(-10)=\Psi(10)=0$$ The boundary of $x$ is ...
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### Plot the lines (nodes) for the given value from NDsolve output

I want to plot lines for a specific single value from the output in Nsolve (we need to find these nodes from the output ufun, then plot them). ...