# 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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### 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, ...
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### Problem Solving Steady State Navier Stokes Equations Using Finite Element Method

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://...
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### 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 ...
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### 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 ...
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### 3D Elastic waves in a glass

Take an empty glass, hit the side, the glass will make a sound that can be recorded using ...
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### 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 ...
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### 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....
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### 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 ...
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### How to change boundary conditions during AceFEM analysis?

I'm trying to prestress a sample by a compressive strain of 10 percent and then stretch it by 30 percent. The way I intend to do this is apply the prestress in one step and then have the code run and ...
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### Error message when trying to solve 2 coupled PDEs using NDSolve

I'm currently facing a problem when trying to solve 2 coupled PDEs. I get the warning messages: NDSolve::fembdcc: Cross-coupling of dependent variables in DirichletCondition[IPF==IPB/10,z==5.] is not ...
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### Modelling a Crankshaft

In the linked documentation, a crankshaft is imported as a GraphicsComplex, which can then be turned into a Finite Element Mesh for the purposes of Finite Element Analysis. I wondered if anyone knew ...
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### Solving Laplace's equation in 2D using region primitives

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 answers define ...
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### Converting .stl files to meshes for FEA

I'm trying to conduct finite element analysis on imported .stl models from SketchUp. I can't seem to generate an ElementMesh. I think it may be something to do with intersecting boundaries, and this ...
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### How to perform adaptive mesh refinement on a 3D element consisting of 4 superimposed meshes on AceFem?

I'm trying to perform adaptive mesh refinement on a body that is composed of 4 separate meshes joined together. The body is composed of the following individual meshes: ...
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### Solving Piecewise Differential Equation using NDSolve (coupling at BC)

I am having some issues in dealing with a system of differential equations. I would like to solve a 1D diffusive heat equation across several regions with different material properties. I now have a ...
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### Solving Nonlinear Heat Equation with initial Conditions

I have the following setup for the linear heat equation on an infinite rod (see below). This is a pretty standard setup and the initial condition is $e^{-x^2}$. This initial condition is not special, ...
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### Ways to decrease computational time

I have created a 2D axisymmetric simulation of the motion of charged particles in an electric field. The electric field is created by a needle attached to a top plate both of which are at -3800V with ...
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### Using Regions, can I model a reflecting wavefront?

I was wondering if I could get Regions and Mathematica's shapes to do all the hard work for me in making a "droplet in a pond" simulation. I do not want the "waves" ...
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### 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 ...
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### Extracting data from InterpolatingFunction 2D surface plot

I would like to directly extract the surface plot data from the solution to a differential equation (using NDSolve). While there are many examples of this I haven't been able to find an example in 2D. ...
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### 2D Oseen equations

Background info: https://en.wikipedia.org/wiki/Oseen_equations ...
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### 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 ...
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### 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. ...
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### 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. ...
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### 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 ...
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### 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 \$...
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### 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,...