On Thu, 2 Feb 2017, Salazar De Troya, Miguel wrote:

> The current implementation of AdjointRefinementEstimator does a
> uniform refinement to obtain an adjoint solution in a richer space.
> This is a necessary condition to obtain an error estimate in a
> quantity of interest. My question is: Is it feasible to perform a
> patch recovery on the adjoint solution and use that in the error
> estimate? Will this be cheaper than the uniform refinement?

Sometimes, and yes.

See AdjointResidualErrorEstimator - you basically combine an error
indicator for the primal solution with an error indicator for the
adjoint solution to get an error indicator for the QoI.

Patch recovery is the default for the sub-indicators, but if you want
this to work well on real physics or even just on problems which
haven't been nondimensionalized, then you need some physics awareness
to get anything like a decent refinement pattern.

You can do that in libMesh by switching out PatchRecovery for
WeightedPatchRecovery with weight functions appropriate to your
physics' Jacobian.  See Vikram Garg's PhD thesis for the details.

Oh, and bear in mind this still gives you an *indicator*, a way to
guide efficient mesh refinement.  If you want a tight stopping
condition then this isn't it.
---
Roy

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