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david.b
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Hello,
for the Poisson problem [itex]Δu = -1[/itex] on a 2D circular disk with [itex]u = 0[/itex] on the boundary, we have
average([itex]u[/itex]) = [itex]\frac{1}{8\pi}[/itex]Area(disk),
which is easy to see, as the solution is quadratic in the polar coordinate [itex]r[/itex]. Does this (or a similar) relation hold for non-circular 2D domains? This problem comes up in Poiseuille fluid flow in tubes of non-circular cross section. Thanks in advance.
David
for the Poisson problem [itex]Δu = -1[/itex] on a 2D circular disk with [itex]u = 0[/itex] on the boundary, we have
average([itex]u[/itex]) = [itex]\frac{1}{8\pi}[/itex]Area(disk),
which is easy to see, as the solution is quadratic in the polar coordinate [itex]r[/itex]. Does this (or a similar) relation hold for non-circular 2D domains? This problem comes up in Poiseuille fluid flow in tubes of non-circular cross section. Thanks in advance.
David
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