# Questions tagged [finite-element]

A means of solving ordinary and partial differential equations. The domain of the problem is broken up into elements, and the solution in each element is expanded in a basis of functions. The Finite Element Method lends itself well to adaptive refinement, irregular geometry, and good error estimates.

885 questions
Filter by
Sorted by
Tagged with
2 views

### What are the practical differences between a Galerkin finite element method vs an orthogonal collocation method?

What are the practical differences between a Galerkin finite element method vs an orthogonal collocation method? The best reference I've found thus far as been a paper titled The Performance of the ...
46 views

### Condition number of finite element stiffness matrix

In the FEM, there are certain applications in which the condition number $(\kappa)$ of the overall global stiffness matrix $(A)$ is computed or reduced by some preconditioner $(P)$. Are there any ...
250 views

### FEM and High Performance Computing

Suppose we want to solve an FEM problem in terms of HPC. What is the most usual way to do it: Using an open-source software like mfem,deal.ii etc.. or, Assembly the system by your own(read mesh file,...
36 views

### implementation of shell elements in a topology optimization algorithm

I am working on developing a topology optimization solver based on the finite element method and I want to add a triangular shell element in it. I used the classic finite element method but I didn’t ...
57 views

### FEM Meshing artifact at nodes with fewer neighbors

I wrote a 2D-FEM solver to solve some diffusion process and wanted to verify my code with a test problem. The input was $f(x,y) = x^2+y^2$ and I applied the stiffness matrix on it to get $\Delta f = 4$...
193 views

### Is the imaginary part needed in this problem?

Before jumping into my question, let me contextualize it. I'm doing numerical simulations of a Helmholtz scattering problem $$\Delta p + \kappa^2 p = 0\, .$$ The incident pressure wave $p^{inc}$ will ...
34 views

### Matrix Calculation Different between Python and Matlab

I am transferring a finite element code from Matlab to Python. A problem occurs at the last step when I try to solve the displacement $U = F/K$. I have checked that the calculated $F$ and $K$ are same ...
69 views

### How to determine global stiffness matrix is constrained or not

Background In solid fem, we often solve $$\mathbf{Ku}=\mathbf{p}$$ where $\mathbf{K}$ is global stiffness matrix, $\mathbf{u}$ is displacement, $\mathbf{p}$ is global load vector. If displacement not ...
34 views

### traction boundary conditions in elasticity

I have a question about implementing traction boundary conditions in 2D and 3D linear elasticity. Consider the picture above. I want to apply traction boundary conditions on the boundary in red. My ...
71 views

### Pressure interpolation in the Q2-P1 element

The Q2-P1 element is one of the popular finite elements for incompressible flow problems in the mathematics community. For this element, the velocity field is approximated using bi-quadratic shape ...
61 views

### Uniaxial stretching solution not uniform in FEM code

I am trapped here for a long time. I wrote a toy Matlab FEM code. I want to run the follow simulation. Mesh Suppose we have a cube, and we divide it into subcube along $x,y,z$ axis, then each subcube ...
91 views

### Solving large sparse system

I am working on a problem with very large sparse matrices. I'd like to compute $A^{-1} B$, that is a crucial part of converting DAE to ODE (and there is no workaround). Here size of $A$ is 2E+5 x 2E+5 ...
130 views

### Weak form of the Navier-Cauchy equation

I am trying to obtain the weak form of the Navier-Cauchy equation, which is $$- \rho \omega ^2 \textbf{U} - \mu \nabla ^2 \textbf{U} - (\mu + \lambda) \nabla (\nabla \cdot \textbf{U}) = \textbf{F}$$ ...
90 views

### FEM with elastic inhomogeneous properties leads to mesh-induced anisotropy

I'm solving an elastic homogenization problem and I'm having problems with mesh artifacts. I would like to first give a brief summary of what I do: I have a system with inhomogeneous (but isotropic) ...
146 views

### $P0$ elements for $H1$

Are there $P0$ (zero degree/constant element) nonconforming methods for approximating solutions in $H1$? More specifically, I have the equation: $$u-f - T\Delta u = 0$$ Which can be interpreted as ...
163 views

38 views

### Lattice spring models vs. finite element models

I am a beginning graduate student in the field of continuum mechanics. It is my understanding that most problems in this field are numerically solved via finite element methods (FEM). However, I have ...
59 views

### Parallel mesh partitioning

When a mesh partitioning takes place and every process works on a part of the mesh is any way to rename the global numbering of nodes(on each process) into a local numbering?Is there any software that ...