# Questions tagged [finite-element-method]

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

612 questions
Filter by
Sorted by
Tagged with
253 views

### 2D Oseen equations

Background info: https://en.wikipedia.org/wiki/Oseen_equations ...
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 ...
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. ...
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. ...
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 ...
121 views

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, ...
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 ...
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 ...
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 ...
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 ...
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: ...
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 $\Omega\in \mathbb{R}^2$: ...
201 views

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 ...
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 ...
121 views

In a simple example I try to solve the heat equation using NDSolve and Method->"FiniteElement". I know that NDSolve gives ...
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 ...
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: ...