CFD Online Logo CFD Online URL
Home > Forums > Main CFD Forum


Register Blogs Members List Search Today's Posts Mark Forums Read

LinkBack Thread Tools Display Modes
Old   July 30, 2001, 04:52
Default Smoothness
Posts: n/a
Hi, Function y = |x| belongs to the class C^0, but does not belong to C^1. And what function belongs to C^1, but does not belong to C^2?
  Reply With Quote

Old   July 30, 2001, 06:41
Default Re: Smoothness
John C. Chien
Posts: n/a
(1). given two curves, jointed at at point, then the smoothness is C^0. Zeroth order continuous, I guess. (2). if you can also find the first order derivative at that point, single-valued, then you have C^1. That is, both the function and its derivative are continuous. (3). So, function x will be continuous, and also has continuous first derivative, and is belong to C^1. (1st derivative is Continuous.)
  Reply With Quote

Old   July 30, 2001, 12:00
Default Re: Smoothness
Posts: n/a
f(x) = abs(x) is C^0 over [-2,+2]


f'(x) = -1 over [-2,0[

f'(x) = +1 over ]0,+2]

and it's undefined at 0.

F(x) = int from{-2} to{x} of (abs(t)) dt = x*abs(x)/2 + 2

is C^1 since its first derivative is abs(x) wich is C^0.

  Reply With Quote


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
Improve smoothness & quality of structured grid quarkz Main CFD Forum 2 March 10, 2007 16:26
Grid's smoothness dwisakti Main CFD Forum 3 September 8, 2000 13:28

All times are GMT -4. The time now is 20:11.