Yes! your explanation clear explains the situation !
Thank you!!!
Jaekwang Kim
2016년 9월 29일 목요일 오전 11시 25분 28초 UTC-5, Wolfgang Bangerth 님의 말:
>
> On 09/29/2016 09:41 AM, JAEKWANG KIM wrote:
> >
> > I thought that the order of error is O(h^p) where h is a mesh-size and p
> > is polynomial degree we use in approximation.
> >
> > So, I thought that if I plot an error with number of mesh in log-log
> > scale, than the graph will show -p slope.
> > However, I the error behaves little bit different from my expectation.
> >
> > For example, I use a step7 tutorial program (which solves Helmholtz
> > decomposition and compares the FEM solution with exact solution.)
> >
> > The error curve showed more steep slope whenever I increase polynomial
> > degree approximation however, the slope is not (-p).
> > I reached slope (-3) when I used fifth-degree polynomial
> approximation...
> > You can check this behavior in attached picture.
> >
> > Until now, I have considered,
> >
> > 1. Mapping(From reference cell to real cell) degree (which is originally
> > set to 1 but I used higher mapping)
> > 2. Instead of Qgauss quadrature, I am using QgaussLobatto Quadrature for
> > any integration over cells.
> > 3. Shape function , again I tried to use QgaussLobatto node point for
> > this)
> >
> > is there any suggestion that I need to fix more?
> > or my first prediction that the slope will show '-p' or error will just
> > behave O(h^p) was wrong?
>
> It ought to be O(h^p), but I *think* what you are plotting is O(N^{-s})
> where N is the number of degrees of freedom. Since N=O(h^{-2}) in 2d,
> what you see is a convergence order of p=2s. Does that explain the
> problem?
>
> Best
> W.
>
>
> --
>
> Wolfgang Bangerth email: bang...@colostate.edu
>
> www: http://www.math.colostate.edu/~bangerth/
>
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