[petsc-users] Penalization vs. setting interior points for Laplace eqn

[Jed Brown]

Barry Smith <bsmith at mcs.anl.gov> writes:

>   I think you can just set the values there. The advantage is
>   simplicity plus it won’t mess up the convergence of the iterative
>   methods as a penalization likely would.

Write the trivial equations for those rows (u = "what_you_want") and
have all the neighboring equations use what_you_want.  That is
"symmetric" removal of those equations.

See this description with notation.

https://scicomp.stackexchange.com/questions/3298/appropriate-space-for-weak-solutions-to-an-elliptical-pde-with-mixed-inhomogeneo/3300#3300


Of course you can use other methods, but I recommend the above because
it maintains symmetry, decouples the boundary dofs, and does not
introduce poor scaling.
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