# 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.

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### Dyadic operations, fourth order tensors and Tensor algebra

I am trying to understand the dyadic operation for a while since I am interested in Elasticity problems. I believe an intuitive understanding (rather than assuming) will give me good problem solving ...
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### Hanging nodes in deal.ii tutorials: how is the continuity constraint imposed?

While looking at step6 of deal.ii tutorials, I decided to try to understand how the constraints coming from hanging nodes are imposed. So I started by watching video lecture 16 by prof. Bangerth As ...
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### Can this volume intgral be expressed as a convex function?

This question is related to the following: https://math.stackexchange.com/q/4151405/685910 - the context is summarized below for clarity. In the setting of convex optimization, I am looking for a ...
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### discretizing surface integral using nodal DG method

I am currently learning nodal DG methods, primarily through the book by Warburton, and am a bit confused on how to handle surface integrals using straight edged elements. On page 187 (and on page 214)...
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### Constrained optimization for non-linear equations in octaveGNU

I have installed Optim1.6.1 package. I would like to solve a system of equations in non linear finite element analysis using constraints as u=1 at certain nodes. u=0 at certain nodes. Typically I find ...
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### Reference for mass matrix assembly

I will now explain what I understand to be the process of a finite element mass matrix assembly. I would like a reference which does something similar, or if I am mistaken about the process please let ...
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### How to implement point source or volume source in finite element implementations

I'm trying to do a simple implementation to study the advection-diffusion-reaction dynamics in a straight pipe. I have points positioned along the length of the pipe (blue dots in the image above). I ...
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### RCM better than Nested dissection? (For FEM discretizations in 2D and 3D)

I realize this might be a too general question but here goes nothing: I am trying different re-ordering strategies and checking the fill-in of $A=LU$. I have 2D ($p=1$, $h=1/40$ on $\Omega = [-1,1]^2$)...
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### What is the weak form of a vector type Laplace equation?

For a scalar variable $u$, the weak form of the following Laplacian: $$\nabla^2 u =0$$ with the assumption that $v$ vanishes at the boundary is $$\int \nabla v . \nabla u \, d\Omega = 0$$ which is ...
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### Validity of algorithm for assembling the finite element global stiffness matrix

This blog post describes an algorithm for constructing the finite element global stiffness matrix as two basic steps: [Step 1] Initialize a table with the elements shared by a pair of connected node ...
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### Is mesh orthogonality important for FEM?

While studying mesh quality metrics in literature and software documentation, I've seen discussions about mesh orthogonality in Finite Volume Method (FVM) contexts, but not for Finite Element Method (...
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### Confused on how Method of Manufactured solutions works?

I am new to computational science and I am trying to wrap my head around how MMS works. I am solving the time independent Helmholtz equation as a simple test of the technique so my starting equation ...
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### Crouzeix-Raviart for Stokes on elasticity form

I have tried to solve the driven cavity problem with incompressible Stokes flow using the standard Crouzeix-Raviart non-conforming P1/P0 element (linear velocity, constant pressure, velocity-nodes at ...
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### Why is FEM theory only ever written down for simplices?

I noticed that in most theoretic literature (Braess, Ciarlet, ...) for Finite Elements, the method is only described in a detailed way for simplex triangulations, while other forms of hexahedral ...
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### FEM port Boundary definition for electromagnetics and wave guides

We are currently in the process of implementing ports in our EM FEM simulation SW. We have come across the definition of boundary conditions for the ports, and we do not understand the equation for ...
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### Finite element method for an equation requiring switch between spectral and temporal domain

Some equations (such as the non-linear schrödinger equation for pulse propagation) are more easily solved in the spectral form, but still need a representation in the temporal domain to calculate ...
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