SUPG advection-diffusion of a rotating pulse in a rectangle#
Donea, J. & Huerta, A. (2003). Finite Element Methods for Flow Problems. \(\S 5.6.1\)
\[\begin{split}
\mathbb{S}
\begin{cases}
\Omega = [0, 1] \times [0, 1] \\
u_0(x) = 0 \\
u_{\text{D}}=0 \\
\textbf{a} = \begin{pmatrix}
-y \\
x
\end{pmatrix} \\
\mathsf{D}=D\mathsf{I} \\
R = 0 \\
J(x,y,t) = e^{-t^{10}}\cos(\pi/2\sqrt{x^2+y^2})\text{H}(1-\sqrt{x^2+y^2})\\
\end{cases}
\end{split}\]