# 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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### Inverting differential equation using finite element methods

tl;dr; How to use FEM tools to extract models needed to invert PDEs. Context In astrophysics, one is interested in so-called 'cosmic archeology' which involves recovering the origin of a given ...
58 views

### How to solve the natural frequency of cantilever beam by mathematical method

I want to calculate the natural frequency of the cantilever beam according to the theoretical method. I find a post on how to solve the free vibration frequency of a cantilever beam with the finite ...
66 views

### Transition to turbulence

I found that a 3D model of viscous flow in a rectangular channel with jump section implemented on the basis of FEM demonstrates a transition to turbulence. We use an algorithm for unsteady flows ...
56 views

### Piecewise Continuous Linear Basis on a Triangular Mesh

Question Given a FEM mesh, I would like to define a set of basis functions anchored to the mesh, so that any piecewise linear continuous function on the mesh can be expanded over that set. Such a ...
157 views

### Laplace equation with robin boundary conditions

I want to solve the following steady state heat transfer problem with robin boundary condition at the bottom: The following is the code for the transient solution, but how should I change the code ...
83 views

### Penalty function on discrete mesh using Laplace-Beltrami operator?

Context I am interested in extending to the ill-condionned regime the inversion of linear equations arising from inverting differential equations which have been solved via 0-splines over a mesh ...
1k views

### How to solve heat equation with Robin type conditions with NDSolve?

Could you help me please to solve following problem! I need to solve one-dimensional heat equation with Robin type boundary conditions. But Mathematica find only constant solution with no dependence ...
3k views

### Future enhancements for the finite element method

How should the finite element method (FEM) framework in the language be extended to be more useful? With the release of version 12.0 alI fundamental FEM solvers (linear, nonlinear, stationary, ...
70 views

### How to numerically obtain the first ten eigenvalues of a 3D Sturm-Liouville problem

I'm trying to numerically obtain the first ten eigenvalues of a 3D S-L problem via NDEigenvalues but with no success. The problem is given by ...
59 views

### 1-D stress (displacement) analysis in annulus by considering viscoelasticity

I am a new Mathematica user, and I was trying to solve a stress (or displacement) field problem in an annulus. Here is the problem in the polar coordinate: The inner radius of the annulus is $b$, ...
55 views

### Define indicator function of mesh elements

Context I would like to (partially) answer my own question here (ok its a bit cheesy but...) Question I am interested in defining an indicator function which value would be 1 on a cell and ...
132 views

### Why can't I use Inactive[D] in NDSolve?

I have a 2D rectangular domain with -L/2 < x < L/2 and 0 < y < D0, which is divided into two parts, with a ...
463 views

### 3D Elastic waves in a glass

Take an empty glass, hit the side, the glass will make a sound that can be recorded using ...
207 views

### Unexpected 'switch' of partial derivatives when differentiating InterpolatingFunction

Bug introduced in 11.3 or earlier and persisting through 12.1.0 or later In short, there is a simple initial boundary-value problem for which NDSolveValue produces an InterpolatingFunction ...
75 views

### Poisson equation and FEM [closed]

I am trying to solve $u_{xx}+u_{yy}=-[(3x+x^2)y(1-y)+(3y+y^2)x(1-x)] e^{x+y},$ for $0<x<1,0<y<1,$ and homogeneous Dirichlet boundary conditions $u(x,y)=x(1-x)y(1-y)e^{x+y}$ by an ...
92 views

### Using FEM and NDSolve

I have to solve the ODE $u''[t]+u'[t]+\sin {(5t)} u[t]=t^3-t$, with $u[0]=0,u[1]=0,$ with a finite element method and then with NDSolve. Finally, I have to ...
72 views

### Plotting a differential equation with boundary conditions

I have a problem with numerical calculation and plotting of differential equation. Now I set a complicated region to set a boundary condition: ...
199 views

### Understanding PeriodicBoundaryConditions

Every thing works fine in a simple example with periodic boundary condition u[ 2,y]==u[0,y] from documentation of ...
100 views

### An ImplicitRegion with a boundary which is an Interpolated Function is not a ConstantRegion

I create an ImplicitRegion from a box-shaped region with one face replaced by a function h[x,y]. If h[x,y] is a "normal" function, e.g. ...
562 views

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### Is it possible to create .stp 3D model from Graphics3D ？

I want to create some 3D solid model by Mathematica, and then export it into stp (step) format for further finite element or finite volume analysis in Fluent/ANSYS or Abaqus. But so far to me, it ...
1k views

### How to create a surface mesh embedded in 3D?

I am working on a problem where I want to optimize current densities on 2D surfaces embedded in 3D to generate magnetic fields. The current density on a surface can be written as a scalar function ...
136 views

### Solving Laplace's equation in 2D using region primitives

Fixed in 12.1 I was looking at examples of solving problems in electromagnetism and ran across this question, which was a great example of just that. However, looking at the Dirichlet condition, both ...
308 views

### Why the mesh generated for NDSolve is different from the final plotted mesh?

When I try the following code to solve the Laplace's equation, the mesh generated by bmesh = ToElementMesh[bmesh] is different from the mesh shown in ...
200 views

### FEM Mesh related errors

Bug introduced in 12.0. Fixed in 12.1.0. I try to solve the simple heat transfer equation but there are some errors at the stage of the pre-processing. ...
94 views

### normal derivative for Laplace equation

I am try to evaluate the Neumann boundary conditions for Laplace equation which define as: dy/dn, where n the external normal vector to the boundary, I have: ...
4k views

### Nonlinear FEM Solver for Navier-Stokes equations in 2D

it's me again. I'm trying to obtain a numerical solution to Navier-Stokes equations in 2D in a non-rectangular region. So far, this guide was very helpful, but he is using finite differences, which is ...
67 views

### NDSolve: Which method for fast moving/spreading wavepackets?

I want to model a wave-packet interacting with a non-linear potential. ...
949 views

### Couple a PDE and ODE in NDSolve

I would like to solve an example of non-stationary heat transfer with a coupled PDE and ODE. Let's assume that we have 1 dimensional bar of length $L$ with uniform initial temperature. The right end ...
66 views

### Numerical solution for PDE [duplicate]

I have got the help from the expert ''Nasser'' to write the code for the PDE with variable coefficients and mixed boundary conditions define on a square domain: ...
115 views

### Variation of the biharmonic equation with Neumann conditions

I am currently writing a script to plot the solution of a variant of the biharmonic equation. In this case the equation I want to solve is ...
94 views

### FEM: how to find 2D flow under external forcing?

I'm trying to sovle a 2D Navier-Stokes equation in a rectangular region with no-flow boundary conditions and an external rotating force $f(x,y)=(-y,x)$. I've got the error message: NDSolveValue::...
132 views

### Problem Solving Steady-State Euler Equations in 2D Using FEM

I am working with gas flows, and my Reynolds number is very large (>10^6). Still as a toy exercise, I solve the steady-state Navier Stokes equations for my volume and it seems to work ok for Reynolds ...
43 views

### Exporting data from an Interpolating Function

Apologies if this question is repetitive, but I have browsed the questions already posed on exporting data from NDSolve and haven't been able to successfully apply the information I found to my own ...
4k views

### Mathematica vs. Comsol for finite element analysis?

Being relatively new to finite element analysis, I was wondering how expert users assess Mathematica's capabilities in solving PDEs via the finite element method compared to other commercial tools (e....
180 views

### Solving a Reaction-diffusion system

I'm just a beginner in Mathematica software. I have version 12. I am looking for a program that will solve a prey-predator system with diffusion. My problem is that I tried a previously posted ...
11k views

### How to solve ODE with boundary at infinity

y''[x] - x y[x] == 0 y[0] == AiryAi[0], y[∞] == 0 The analytic solution to this ODE is the Airy function y[x] == AiryAi[x] ...
84 views

### How to tell mathematica polar coordinates belong to mesh?

Context I want to solve a PDE via FEM on a Disk. If I use a Square I can write ...
731 views

### Gravitational potential created by a thin disc using FEM and NDSolve

Context I would like to compute the torque that a (thin) disc applies onto a ring. I.e. I would like to try to understand what is the impact of this outer ring on the inner disc in the simulation ...
193 views

### Not sure how to set up the Laplacian/Poisson Equation

As stated, I am having trouble trying to set up a Laplacian/Poisson Equation. I have boundary conditions with this too, and I've tried using the DirichletCondition function, but I don't know what I'm ...
121 views

### Why can't I solve a system of four third-order partial differential equations using NDSolve?

I solve the problem of optimal control. First, I solve a system of two equations (with respect to the variables p, q, V, n) with already optimal conditions (Kopt and Sopt) to check whether it is ...
101 views

### Numeric Solution for 1-D ODE with only Neumann conditions

I tried to solve a simple ODE with only Neumann conditions like But obviously this doesn't work. I must add a useless DirichletCondition to make it work I have verified that the solution is correct, ...
82 views

### Problem Solving Steady State Navier Stokes Equations Using Finite Element Method [closed]

I am using MMA 12.0.0 on a Mac running OS version 10.13.6. Before attempting my own problem I am attempting to follow exactly the code in the FEM Documentation Tutorial, as an exercise: https://...
87 views

### System of pde with Neumann boundary conditions

The Ginzburg-Landau equation for a system of squared superconductor with a slit in presence of a uniform magnetic field can be written as a sort of continuity equation with Neumann boundary conditions ...
190 views

### The NDSolvevalue of MMA can not be used to solve the finite element problems according to the stress boundary conditions

The NDSolvevalue of MMA can well solve the finite element problems according to the displacement boundary conditions ...
178 views

### Where to get the detailed code of MMA for grid mesh

I know DelaunayMesh can triangulate the specified area, but I can't see the code and partition idea of this built-in function. I want to know how to get the source ...
53 views

### Numerical Issues Using Results of NDSolveValue

I am solving Laplace's Eqn. (Cartesians) in 2D in a region which is infinite in x, semi-infinite in y, and bounded by a function of x (h[x] in my code) close to y=0....
353 views

### Boundary Problems

I am trying to study what happens to a wave as it passes different boundaries. This is the working wave equation defined on a plane ...