To reiterate what Matt is saying, you seem to have the exact solution on a 10x10 grid. That makes no sense unless the solution can be represented exactly by your FE space (eg, u(x,y) = x + y).
On Mon, Oct 8, 2018 at 9:33 PM Matthew Knepley <[email protected]> wrote: > On Mon, Oct 8, 2018 at 9:28 PM Weizhuo Wang <[email protected]> wrote: > >> The code is attached in case anyone wants to take a look, I will try the >> high frequency scenario later. >> > > That is not the error. It is superconvergence at the vertices. The real > solution is trigonometric, so your > linear interpolants or whatever you use is not going to get the right > value in between mesh points. You > need to do a real integral over the whole interval to get the L_2 error. > > Thanks, > > Matt > > >> On Mon, Oct 8, 2018 at 7:58 PM Mark Adams <[email protected]> wrote: >> >>> >>> >>> On Mon, Oct 8, 2018 at 6:58 PM Weizhuo Wang <[email protected]> >>> wrote: >>> >>>> The first plot is the norm with the flag -pc_type lu with respect to >>>> number of grids in one axis (n), and the second plot is the norm without >>>> the flag -pc_type lu. >>>> >>> >>> So you are using the default PC w/o LU. The default is ILU. This will >>> reduce high frequency effectively but is not effective on the low frequency >>> error. Don't expect your algebraic error reduction to be at the same scale >>> as the residual reduction (what KSP measures). >>> >>> >>>> >> >> -- >> Wang Weizhuo >> > > > -- > 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/> >
