Boundary Value Problems/Lesson 8: 2-D Potential Equation

Rectangular Domain (R²)

$\displaystyle u_{xx}+u_{yy}=0$

Disk Domain (Polar)

$\displaystyle u_{rr}+{\frac {1}{r}}u_{r}+{\frac {1}{r^{2}}}u_{\theta \theta }=0$

Example of Potential equation on semi-annulus.

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