Hello,(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Constant source Poisson eq in 2D, Dirichlet BC, average value?

Loading...

Similar Threads for Constant source Poisson |
---|

A Solving linear 2nd order IVP non-constant coefficient |

A Damped Thermal Oscillations |

I When is a Constant a Solution to a Differential Equation |

**Physics Forums | Science Articles, Homework Help, Discussion**