Linear stationary system of 2 partial DEs, numerical implementation

1. Oct 28, 2008

motorhue

Hello.
I have a fluid in a rectangular basin, driven by stokes drift at the southern wall. The problem is formulated as follows:

\begin{align*} -U_y+V_x &= g_1(x,y) \\ U_x+V_y &= g_2(x,y) \\ U(x=0)=U(x=M)&=V(y=0)=V(y=N) = 0 \end{align*}

Here, g_1 and g_2 are known functions of the horisontal coordinates x and y. M and N are east and north boundary, subscript denotes derivatives.

My question is how can I implement this numerically? If I reduce to one variable I get a problem implementing the boundary conditions on the other variable. I believe it should be doable with a rather straightforward matlab routine?

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