# 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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### Nonlinear PDE with a trivial and nontrivial solutions: how to?

I am solving the following PDE: eqMain = D[z[x, y], {x, 2}] + D[ z[x, y], {y, 2}] - (a - x/(x^2 + y^2 + 0.0001))*z[x, y] - z[x, y]^3==0; with the zero ...
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### Problem with NDSolve for 1st order non-linear system of PDEs

I wish to solve the PDE system \begin{align} x_u^2+y_u^2+\left(xx_u+yy_u \right)^2&=1\\ x_v^2+y_v^2+\left(xx_v+yy_v \right)^2&=1 \end{align} subjected to $x(0,v)=0$ and $y(u,0)=0$. However, ...
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### SolidMechanicsStress returns, that the stress is equal to zero

Bug introduced in 13.1 and fixed in 13.2.0 I am trying to compute a deformation and a stress of a material with a custom material law. I have successfully computed the deformation using ...
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### Solving 3D Nonlinear Integral Partial Differential Equation

I am trying to solve Equation number (1.2) numerically in MATHEMATICA. This equation is solved in the papers https://arxiv.org/pdf/2205.05193.pdf, https://arxiv.org/pdf/2202.13264.pdf, and https://...
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### Create a domain for an Hexahedron with the floor replaced with an Indian Burial Mound

I am trying to create an acoustic model domain for a small park that contains an Indian burial mound. The park is laid out using a 3D cartesian coordinate system in units of meters. A Hexahedron ...
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### Can NDSolve be initialized with a close solution?

I have a set of 4 first order ODE with 4 initial conditions to be met. It models a simple damped pendulum like the one described here. What changes is the damping term and I switched to first order ...
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### Is it possible to remove an element during computation in AceFEM?

The title says it all. I know there have been a lot of enhancements in the recent versions of AceGen/AceFEM. I would like to know if there is a possibility of removing an element during computation (...
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### 1D diffusion problem: Troublesome NeumannValue

Bug introduced in 13.1 or earlier and fixed in 13.2.0 Mathematica solves the diffusion problem (two Neumann-conditions) ...
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### Select part of an ElementMesh

modified For an, examplary simple, ElementMesh ...
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1 vote
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### NDSolve with piece-wise function and BVP

How to numerically solve a system of differential equation with boundary conditions and piece wise affine functions ? Consider the following system of differential equations from some optimal control ...
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1 vote
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### Building a structure out of cubes one block at a time

I have simplified code in which the motion of a point charge is simulated N times (one particle at a time) in a static electric field. When the point charge comes to rest (using WhenEvent boundary ...
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### Solve 3D convection-dominated PDE with discontinuous coefficient, without tiny mesh

I'm trying to simulate a self-propelled particle diffusing on a disk. The direction of the self-propelled velocity $\vec{v_A}$ doesn't change, while it speeds up at the boundary and slows down at the ...
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### BoundaryMeshRegion Error: Boundary surface is not closed

I am trying to create a BoundaryMeshRegion comprised of many cubes with random locations, in a relatively small region. I have had success implementing my technique for a smaller number of cubes (say,...
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### Calculating the 3D magnetic vector field of a permanent magnet, with shape given by STL File

following my earlier question Link, I am trying to calculate the magnetic field of a permanent magnet. The shape of the magnet was generated with FreeCAD and is provided to Mathematica by an .STL file....
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### Monte Carlo Simulation of Charged Particles in Non-Uniform Electric Field

I have a code (provided below) which simulates the motion of an ensemble of charged particles which are subjected to a complex static electric field which passes through some aperture in a metallic ...
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1 vote
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### Different boundary conditions

I have a problem regarding the definition of multiple boundary conditions in AceFEM. I am dealing with coupled problem simulations (displacement and magnetic potential) and therefore I have to apply ...
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