# Tagged Questions

Tag for the usage of "FiniteElement" Method embedded in NDSolve and implementation of finite element method (fem) in mathematica.

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### FEM: user material subroutines (UMAT in ABAQUS), mechanics

Just a quick question (mainly for those who are also familiar with ABAQUS or other comparable FEM programs and non-linear modelling of mechanical behavior, e.g., plasticity). Is there any module in ...
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### Kernel quits without error in NDSolveValue

I am using the latest 10.1. The following single line command makes the kernel quit without error message (just a beep): ...
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### MinMax function (Mathematica v10.1.0) conflicts with NDSolveFEMMinMax?

Some problem in v10.1.0 (Windows 8.1 x64) and the new MinMax... ...
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### Problem with ElementMeshAlteration to create a 2nd order ElementMesh

After working on this 2D domain, I'm trying to reproduce the same ideas to create a mesh of a sphere composed of QuadElement, instead of more simple and common ...
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### NDSolve and FEM support for non conformal meshes of a disk [with Kernel crash]

I want to create an ElementMesh for a disk. For my specific scenario, some author advise to use a regular mesh, where the radial and tangential directions are ...
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### Error message for FEMStiffnessElements

I am trying to solve this pde numerically with Mathematica: ...
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### FEM: how to choose FEM element type

I am asking myself if there is any simple option for choosing the element type for the mesh generation WITHOUT explicitly creating coordinates and then the mesh. Minimal example: here I would like ...
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### PDE solution does not satisfy Neumann boundary conditions using NDSolve

I am trying to solve the free particle Schrodinger equation in 1D (hbar =1, Energy = 1, mass = 1), But specifying conditions only on x==0: ...
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### Join Two Element Meshes

Let's say I have two element meshes defined as the following: ...
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### Solve a PDE over a region defined by a Bezier patch

I am using NDSolve to find the solution to a PDE over an arbitrary domain. The domain is specified by a Bezier patch. ...
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### Long running ToElementMesh with very “large” domains

I'm trying to solve a system of PDE over a large domain. This doesn't means I need to have a huge amount of mesh points and mesh elements to discretize the domain. Just that the domains has a big ...
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### FEM - how should I impose periodic boundary conditions in pure space problems?

I have searched other threads, but I was not successful in finding an answer I could understand. Right to the point: how do I impose correctly periodic behavior on the edges of the rectangular ...
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### BUG: Problems generating FEM ElementMesh in 1-D

fixed in 10.1 (windows) I'm trying to build an ElementMesh for a simple 1-D problem. First, I build the boundary ...
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### Dirichlet conditions being ignored

I have the following domain: ...
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### Toroidal implicit region looks weird

I have the following toroid surface: ...
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### How discretize a region placing vertices on a specific non-uniform grid

Given a generic region, for example: Ω = ImplicitRegion[ 2 x^2 + 3 y^2 + 2 x y - 2 <= 0 ∧ x^2 + y^2 > .1, {x, y}]; and a non-uniform grid, for ...
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### Trouble understanding NeumannValue and Inactive/Formal PDEs

I read all documentation about the Finite Element Method in Mathematica 10, and I read some questions here, but I'm still unable to properly understand how to use the ...
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### representation of custom deformation on a meshgrid

I am trying to represent 2D deformations on a rectangular grid. In Mathematica 10, there is a method to solve the elastic differential equations and then represent the deformation as presented here: ...
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### Missing links in usage statements

The integration of the documentation center does not seem to be complete on my machine. I often access the documentation center via the usage statement links. ...
213 views

### Problem with Neumann condition in quarter disc

Bug persists through version 10.1 So I'm following the available examples in version 10 for FEM, The plane stress operator is shown as this ...
383 views

### How to create subregions for the NDSolve FEM Solver

I am trying to create a 2d region consisting of two subregions. The inner region has several holes, where boundary conditions are applied. The figure shows the idea. I have tried to create this ...
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### Puzzling NDSolve[] behavior for PDE (smooth solution, inconsistent with boundary conditions)

Consider the following: NDSolve[{D[z[x, y], x, x] + D[z[x, y], y, y] == 0, z[x, 0] == Sin[x], z[0, y] == Cos[y]}, z[x, y], x, y] {{z[x, y] -> ...
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### How to solve a PDE with Robin Boundary Condition inside considered region?

I'm trying to solve the heat diffusion equation in cylindrical coordinates. The main problem is that I would like to include the Robin Boundary Condition inside considered region in order to simulate ...
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### How to solve a nonlinear coupled PDE with initial and some boundary values

I would like to solve the following nonlinear coupled PDE with a mix of initial conditions and boundary values: ...
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### Calculating a potential function using the finite element method

This is my first attempt to use the Finite Element method available in version 10. There are questions and I am very open to suggestions. My example is flow around a cylinder which is a well known ...
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### Error when extending 1-dimensional PDE to 2 dimensions

I want to calculate how magnetic flux is trapped in a superconductor near the interface superconductor/vacuum. This problem already was solved analytically by J. Pearl for cylindrical symmetry (if ...
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### FEM: Nicer Element Shape for Spherical Region

I'm trying to generate a mesh for later use in the Finite Element Method of the DSolve command. It is basically a parallelepiped with a spherical indentation. I'm ...
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### How to set the boundary fixed and apply the Young's modulus in Mathematica's FEM? [duplicate]

Provided the drawing .stl is given, and the Young's modulus is know, how to start a FEM vibration mode test in Mathematica? The boundary is required to be fixed and the interested focus is on the ...
620 views

### Test a wooden board's vibration mode

Here is a wooden board, with dimensions shown on the picture below. How we can use Mathematica's newly build-in finite element analysis features to show the different modes of its vibrations. Assuming ...
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### Solving a nonlinear PDE with Mathematica10 FEM Solver

I am trying to solve a system of coupled nonlinear PDEs in a rectangular region with the new FEM solver in Mathematica 10. However, I come across an error stating NDSolveValue::femnonlinear: ...
How do I solve the PDE with boundary value like this $$u(t,x,y)=0, \textrm{when } F(x,y)=0$$ using DSolve? As a specific example, I want to solve heat equation \frac{\partial u}{\partial ...