Monday, November 11, 2013

Laplace eq on a sphere in 3D

I use example from Chernyshenko-Olsh. paper for the 3D case:

$u=12(3x_1^2 x_2- x_3^3)/||x||^3)$

$f = -(72(x_2^3-x_2^2 x_3+x_2 x_3^2+x_3^3-x_1^2(5x_2+x_3)))/||x||^5) + u$

Details
5-point scheme of second order was used to integrate inside the tetrahedrals.

Due to memory/processing time I was not able to use $h< 0.05$

Result



Convergence plots

band of width 3h


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