Thanks Matt - this is very helpful. On Sun, Oct 14, 2018, 7:13 PM Matthew Knepley <[email protected]> wrote:
> On Sun, Oct 14, 2018 at 3:56 PM zakaryah <[email protected]> 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/> >
