# Questions tagged [finite-element-method]

Usage of the Finite Element Method embedded in NDSolve and details on the implementation of the fem in mathematica.

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### Boundary condition for heat equation in polar coordinates deduced with L'Hôpital's rule fails for method of lines, but works well for FDM

Update I manage to find a way that resolves the problem. I'd like not to make this solution public for the moment so other answerers will have more chance to get the bounty. Here's a hint: it's a ...
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### NDSolve can't find Neumann Value on domain

Trying to solve for the temperature around an axisymmetric thin disk. Edges of the domain are DirichletConditions which work fine, but the solver can't find the <...
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### Boundary condition error with 2D Poisson equation

I'm trying to solve Poisson's equation for the temperature difference ($\Delta T$) between two layers with known conduction between them. The layers have conductive elements spaced in a hexagonal ...
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### Face-based discrete directional derivative on triangular mesh

For a scalar function $f$ defined on the faces of a triangulated surface $M$, and a vector field $\mathbf{F}$ on its tangent space, is there a built-in or simple way to get the derivative of $f$ in ...
1 vote
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### Solving 2D Rotational GPE and Finding Overlap Of Solutions

I want to generate those figures (fig 2) by solving equation no 7 from this paper https://arxiv.org/pdf/1906.06327 for different rotation values (\Omega) and ...
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### Solving a System of Nonlinear PDEs with Finite Element Method (from paper Materialia 1 (2018) 78–88)

I am trying to solve a system of nonlinear PDEs using the finite element method in Mathematica. The system consists of equations for vacancies (V) and self-interstitial atoms (SIAs) and corresponds to ...
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### Orientation of 1st order 2D boundary mesh is counter-clockwise but 2nd order one is clockwise, any deep reason?

Consider this toy example: ...
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### Creating QuadElements from a set of points

I am new in Mathematica. Is it possible to create QuadElements from a set of points? In this link there is an explanation for creating triangleElement. Suppose I have only coordinates of my points as ...
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### Issue with Eigenfunction Expansion Method for Solving ODE in Mathematica

With the following Mathematica code, I am trying to solve a differential equation (ODE) using the eigenfunction expansion method. Unfortunately, when I compare the ...
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### Different eigenfunctions are generated if I change the number of eigenfunctions I want to have

I was experimenting with solving differential equations using eigenfunction expansions. I was troubled by the fact that my solution was very different from the solution produced by ...
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### Why is there a difference between the results using DirichletCondition and directly given boundary condition?

The simulation code ...
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### Boundary conditions being ignored or not obeyed by NDSolveValue

I have the following coupled ordinary differential equations (drift-diffusion with a loss term) that I am having trouble with solving. One of the boundary condition I supply is being ignored. When I ...
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### How to Solve a Piecewise PDE System in Mathematica?

I'm working on a problem involving the transverse vibration of a piecewise beam system. The system consists of two segments with different properties (length, Young's modulus, second moment of area, ...
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### Finite Element beam model with three supports

I have defined a 3 support beam, with a uniform load over part of the span. The end BC are simple to define - deflection and moment = 0. The midspan BC for deflection =0 but but the moment can not ...
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### Issue with solving coupled partial differential equations with NDSolve for certain boundary conditions

I am trying to solve the coupled PDEs for functions u, v and w. The main problem I am facing is that I am unable to understand how to input boundary condition of this type in NDSolve: D[u[x, y], y] + ...
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### Finite ELement Model - simple beam, ends pinned, uniform load over 1/2 of beam, getting several errors

here is the code I am using - having issues getting started in FEA for this simple beam model. The problem is simple - I have looked at posted examples of MMA FEA, but they are all 2D and 3D problems....
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### AceFEM-generated mesh versus Mathematica mesh: How to extrude 2D mesh to create a 3D mesh in AceFEM

The packages MeshTools (@Pinti) and FEMAddons seem to feature similar functions. I sometimes had strange (i.e. inconsistent results when meshing would work/not work without changing anything). Which ...
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### Boundary сonditions specified in different domains

I am modeling mass transport phenomena involving convection and diffusion within a two-dimensional box. The box has a height ranging from 0 to h along the y-axis and is divided into two domains along ...
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### NDSolveValue - states fewer dependent variables than equations for simple FEM beam model & variables not same shape

This is a simple FEM beam model. Supported at both ends, uniform load. Nothing complex. error message - "There are fewer dependent variables, {u[x]}, than equations, so the system is ...
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### NDSolveFEM 3D problem [closed]

I solved Laplace's differential equation in 2D with functions from the NDSolveFEM package and everything worked fine, but when I extended it to 3D, it doesn't work ...
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### How to define styles for a mesh based on a function of element index

My main objective is to have control over style of each element in a mesh. I don't quite understand how ElementMeshToGraphicsComplex works. It looks very cool and ...
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### EM Wave Equation: Insufficient initial conditions for NDSolve?

I am trying to model a EM wave propagation through a region of free space. However, Mathematica tells that there are insufficient initial conditions, even though I specify all values at ...
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### Nonlinear FiniteElement method (Inactive-form) : PDE-Discretization fails

In the documentation Nonlinear Finite Element Method Verification Tests an analytical solution of the problem is given ...
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### Schrödinger equation for the Morse potential (DEigensystem)

I have tried to solve the Schrödinger equation for the Morse potential using Mathematica. I am using Mathematica 12, and I have written the following code: ...
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I am trying to solve the following Fokker-Planck equation using NDSolveValue: $$\partial_t P(x,t) = -\partial_xJ$$ where $$J = -D\partial_x P(x,t) - (D/k_BT)\partial_xW(x)$$ where we assume D,T ...