[petsc-users] Implementing FEM with PLEX/DS/SNES

[zakaryah]

Thanks Matt - this is very helpful.

On Sun, Oct 14, 2018, 7:13 PM Matthew Knepley <knepley at gmail.com> wrote:

> On Sun, Oct 14, 2018 at 3:56 PM zakaryah <zakaryah at gmail.com> wrote:
>
>> Hi Matt,
>>
>> > Can you explain more about this source term? It sounds like a bunch of
>>>> > delta functions. That
>>>> > would still work in this framework, but the convergence rate for a rhs
>>>> > with these singularities
>>>> > is reduced (this is a generic feature of FEM).
>>>>
>>>
>> Can you elaborate on this, or suggest references?  In the context of
>> elasticity, does this mean that convergence for problems using node forces
>> us generally worse than with the equivalent body forces?  Thanks!
>>
>>>
> Think of the simplest example, which is a Laplacian with a delta function
> source. The solution is the Green's function 1/r.
> This is singular at the origin (and not in the FEM space), and the
> standard FEM bases are bad at approximating 1/r near the origin.
> Babuska has a bunch of papers on this. Now what does "worse" mean in the
> context of node forces vs tractions? It means that the
> convergence of your computed solution, as you refine the mesh, is slower
> to the true solution of the node forces problem then it is
> to the true solution of the tractions problem.
>
>    Matt
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
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