Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation
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Numerical examples

We consider the following four convection-diffusion operators together with homogeneous Dirichlet boundary conditions on the unit-square:

$ T^{\alpha} := -\Delta +b\,\partial_{x},$

$ T^{\beta} := -\Delta +\frac{\displaystyle b}{\displaystyle\sqrt{2}}\left(\partial_{x}+\partial_{y}\right),$

$ T^{\gamma} := -\Delta +b\cos{\omega}\,\partial_{x}+b\sin{\omega}\,\partial_{y},$

$ T^{\delta} := -\Delta -4b\,x(x-1)(1-2y)\,\partial_{x}+4b\,y\,(y-1)(1-2x)\,\partial_{y},$

where $ b$ is a constant ( $ b=0,10^1,...,10^6,10^8$). The angle $ \omega\in[0,\frac{\pi}{2}]$ describes for $ T^{\gamma }$ the direction of the convective vector field with respect to the $ x$-axis.


Frank Kiefer