Dear Krishna,

There is also this long-standing pull request
https://github.com/dealii/dealii/pull/8196 
<https://github.com/dealii/dealii/pull/8196>
that hooks into the Verdict library to do mesh quality assessment. One day, 
hopefully in the not too distant future, I’ll get back to integrating it into 
the deal.II library. But you could always extract the salient portions of that 
code for your purposes.

Best,
Jean-Paul

> On 15 Jan 2020, at 18:31, Martin Kronbichler <kronbichler.mar...@gmail.com> 
> wrote:
> 
> Dear Krishna,
> 
> We have recently added one such function, namely 
> GridTools::compute_aspect_ratio_of_cells(),
> 
> https://dealii.org/developer/doxygen/deal.II/namespaceGridTools.html#a2a9d8801d952ea8afa9ec1573229a329
>  
> <https://dealii.org/developer/doxygen/deal.II/namespaceGridTools.html#a2a9d8801d952ea8afa9ec1573229a329>
> Best,
> Martin
> On 15.01.20 18:26, Krishnakumar Gopalakrishnan wrote:
>> In the results/extension section of Step-6 as well in Step-49, there is a 
>> great deal of discussion about obtaining good meshes are for a problem, with 
>> the caveat that this is a highly specialized topic. Step-49 is full of 
>> warnings about things that can go wrong when applying certain 
>> transformations, and it seems to implant doubts in my mind that my meshes 
>> are never going to be correct :)
>> 
>> 
>> Given this, in the spirit of the Kelly Indicator for solution errors in a 
>> cell, is there a similar single-metric for the quality/goodness of each cell 
>> in a mesh? Maybe there is something based on the smallest internal angle (to 
>> prevent slivers, for Jacobian of the mapping to be invertible, to prevent 
>> inverted cells etc).
>> 
>> 
>> After all, error estimation is a complicated topic. nevertheless the Kelly 
>> Indicator seems to do a reasonable job for quite a few equations. If 
>> currently not implemented in Deal.II, is there any journal article that 
>> discusses research in this direction?
>> 
>> 
>> 
>> Krishna
>> 
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