On 3/11/20 7:57 AM, Krishnakumar Gopalakrishnan wrote:
In Step-21 tutorial, we have a statement that starts with the following
(emphasis is mine):
/_"Given the saddle point structure_ of the first two equations and
their similarity to the mixed Laplace formulation we have introduced in
step-20
<https://nam01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdealii.org%2Fdeveloper%2Fdoxygen%2Fdeal.II%2Fstep_20.html&data=02%7C01%7CWolfgang.Bangerth%40colostate.edu%7Ccd1596e29c4a427d467808d7c5c41aa8%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C1%7C637195318357612315&sdata=1Y%2Fp8SQc%2F2YETGls%2FU5J8XPtkz5JLEZW%2FYGdLEnM9rc%3D&reserved=0>"/
/
/
//
It would be helpful if someone could explain the saddle-point structure
of the problem (and/or point to some easily readable online resources).
> [...]
However, I'd really appreciate if there was some "simple test" or
practical advice to determine whether our own PDEs and DAEs belong to
the saddle-point category or not, i.e. how to detect the presence of
saddle-point nature of the PDEs, just simulate with Qp elements and look
for a checkerboard pattern in the results?
I thought we had addressed this a while ago already:
https://github.com/dealii/dealii/pull/9470/files
Is that not enough? Or is the issue that the text added there just says
"indefinite", whereas you are looking for the term "saddle point problem"?
I think a good approximation is that
saddle point problem = indefinite + symmetric
We could presumably add this there.
Best
W.
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Wolfgang Bangerth email: [email protected]
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