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.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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