On 12/26/20 3:06 AM, Konrad Simon wrote:
What one can also do is just constrain one DoF to a specific value (this would
also remove rigid motion in elasticity). But think about your solution
variable: If it is in the Sobolev space H^1 then point evaluations may not be
defined for dimension larger than 2. Similarly if, for example, the pressure
in a mechanical or fluid problem is often just in L^2. Point evaluations do
not make sense there at all.
Right, this is the correct approach: Constrain a single degree of freedom to
zero (or any other value you choose) and solve the problem. Then you can
subtract the mean value of the solution *after* solving the linear system.
(See VectorTools::subtract_mean_value and VectorTools::compute_mean_value.)
If you're uncomfortable with the ill-posedness of taking a point value, you
can also take the mean value along a small segment of the boundary (step-1) or
a small part of the domain. But in practice, this is not necessary and
Konrad's solution is what everyone seems to be doing.
Best
W.
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