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

[Matthew Knepley]

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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