[Users] Meeting minutes

[Erik Schnetter]

On Tue, May 24, 2011 at 12:00 PM, Ian Hinder <ian.hinder at aei.mpg.de> wrote:
>
> On 24 May 2011, at 17:50, Erik Schnetter wrote:
>
>> On Tue, May 24, 2011 at 2:11 AM, Ian Hinder <ian.hinder at aei.mpg.de> wrote:
>>>
>>> On 23 May 2011, at 23:49, Bruno Coutinho Mundim wrote:
>>>
>>>>
>>>>> * Bruno still has troubles with RotatingSymmetry180 when using the
>>>>> development version of ET for the BBH example (parfile is in subversion)
>>>>> * will try running without RotatingSymmetry180
>>>>
>>>> Just got the results: no problem without RotatingSymmetry180.
>>>
>>> OK good, so we know where the problem is.
>>>
>>>>
>>>>> * convergence in norms is bad, somewhat better in 1D data for a short
>>>>> time after simulation startup
>>>>
>>>> A closer look into the initial data revealed that both the l2-norm of
>>>> the hamiltonian constraint and its value along the x-axis converge to
>>>> the expected order, 4th order. This convergence is not observed anymore
>>>> in the very next coarse step when the comparison is done again.
>>>
>>> The time prolongation is only 3rd order accurate so I wouldn't expect convergence at 4th order.
>>
>> Time prolongation is second order accurate.
>
> As I understand it, the three-point interpolation (from the three timelevels) is locally 3rd order accurate, but when you add up T/dt of them to get to a fixed time, you reduce the order to 2.  I tend to get confused about this, but do we agree on this?

Counting orders is always difficult. There are three time levels for
each point, which prescribe a parabola. This is used to interpolate,
with an error term in O(dt^3). If you add up T/dt to get to a fixed
time, the error is in O(dt^2), which I would call "first order
accurate".

-erik

-- 
Erik Schnetter <schnetter at cct.lsu.edu>   http://www.cct.lsu.edu/~eschnett/