An archived instance of discourse for discussion in undergraduate PDE.

Numerical L-shaped Poisson

Mark

Suppose we wish to solve Poisson's equation $u_{xx}+u_{yy}=-1$ on the L-shaped region shown below subject to zero Dirichlet boundary conditions.

Use a rectangular grid with $\Delta x = \Delta y = 1/2$ to write down five equations in five unknowns to approximate the solution. Solve the equations.