[petsc-users] Increasing norm with finer mesh

[Mark Adams]

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 <knepley at gmail.com> wrote:

> On Mon, Oct 8, 2018 at 9:28 PM Weizhuo Wang <weizhuo2 at illinois.edu> 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 <mfadams at lbl.gov> wrote:
>>
>>>
>>>
>>> On Mon, Oct 8, 2018 at 6:58 PM Weizhuo Wang <weizhuo2 at illinois.edu>
>>> 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/>
>
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