# Tagged Questions

The tag has no usage guidance.

27 views

### How to form the stiffness matrix for the Poisson equation using a spectral method

This is a follow-up question to How do I form the Chebyshev differentiation matrix in MATLAB? The goal of the following code is to solve the Poisson problem: ...
76 views

### Finite element error for second order ODE at nodes equal to zero

I coded a finite element method with linear basis elements for the problem $$-u'' = f(x), x\in[0,1], u(0) = u(1) = 0$$ The nodes are uniformly spaced and I will denote them as $x_i$. I initially ...
54 views

### Does a mixed method solve this elliptic pde exactly if the source function is piecewise polynomial?

Let $\Omega\subset \mathbb{R}^d$, $d\in \{2,3\}$ be an open bounded polygonal/polyhedral set. Suppose I want to solve the following pde \begin{align*} \vec{q}+\vec{\nabla}u &=0\,&x&\in \...
40 views

### Manufacturing a solution for non-smooth coefficients in elliptic problems

This question is a continuation of this answer (I can't comment) If we were going to manufacture a solution for a problem with discontinuous coefficients, I understand that the solution should have ...
45 views

69 views

### How do I avoid divide-by-zero when solving the Poisson equation with Fourier transforms?

I wanted to try to implement part of the method in the following article using Fourier transforms. http://www.shodor.org/media/content/jocse/student_submissions/nocito2010/nocito2010_pdf Right now I ...
20 views

### Gradient convergence on a checkerboard domain in finite element

I've got an elliptic problem in a domain with two materials in a checkerboard arrangement. Both materials are highly dissimilar, being one much more compliant than the other. If I use classic linear ...
44 views