Advection-Diffusion Problem

$$ \left\{ \begin{aligned} -\alpha \Delta u + \vec{\beta}\cdot \nabla u &= f \quad \text{in } \Omega=[-1,1]\times[-1,1], \\ u &= g \quad \text{on } \partial\Omega, \end{aligned} \right. $$ with source function

$$ f(x,y) = \frac{5\pi^2}{4}\cos\left(\frac{\pi x}{2}\right) \sin\left(\frac{\pi y}{2}\right) $$

and Dirichlet boundary condition

$$ g(x,y) = 0 $$

Configuration

$\alpha=$

$\beta_x=$ $\beta_y=$

Custom variables

$a=$ $b=$ $c=$