Serving the Quantitative Finance Community

 
User avatar
SemiMartingale
Topic Author
Posts: 0
Joined: March 18th, 2008, 10:40 am

finite element solution

July 4th, 2008, 4:50 pm

Does someone has a copy of this article please ? :"Finite element solution of diffusion problems with irregular data" from R. Rannacher.It is not on Rannacher's homepage and I didn't find it for free on the web.
 
User avatar
Cuchulainn
Posts: 20254
Joined: July 16th, 2004, 7:38 am
Location: 20, 000

finite element solution

July 5th, 2008, 6:27 am

It's not a direct answer to your question but Plan B is to use implicit Euler and Richardson extrapolation to get stable, second order approximation in time and no oscillations (the Lawson-Morris method) that you get with Crank Nicolson near the strike and barrier.Rannnacher is basically Euler for the first few steps and then CN after that. IMO is it a workaround to solve the 'wiggly wigglies'. I have not seen it used it much in general.The LM method is described this the thesis in this forum Sheppard (scroll to 1st post) And it's easy to program.A number of quants use this method now.It's only half an answer but I do not think the Rannacher paper is freely available. Why not contact the local university that subscribe to?
Last edited by Cuchulainn on July 4th, 2008, 10:00 pm, edited 1 time in total.
 
User avatar
SemiMartingale
Topic Author
Posts: 0
Joined: March 18th, 2008, 10:40 am

finite element solution

July 7th, 2008, 5:25 pm

thank you very much for your answer . In fact, I found another paper on the subject and I used a Rannacher technique 1/4. It works quite well. If I still have troubles, I will move to your solution.
 
User avatar
Cuchulainn
Posts: 20254
Joined: July 16th, 2004, 7:38 am
Location: 20, 000

finite element solution

July 7th, 2008, 7:39 pm

QuoteOriginally posted by: SemiMartingalethank you very much for your answer . In fact, I found another paper on the subject and I used a Rannacher technique 1/4. It works quite well. If I still have troubles, I will move to your solution.You're welcome. Do you have a link to this?
 
User avatar
SemiMartingale
Topic Author
Posts: 0
Joined: March 18th, 2008, 10:40 am

finite element solution

July 8th, 2008, 1:36 pm

Here is the web page to get the file:http://people.maths.ox.ac.uk/~gilesm/finance.htmlThe name of the article is: M.B. Giles and R. Carter. `Convergence analysis of Crank-Nicolson and Rannacher time-marching', Report NA-05/16, Oxford University Computing Laboratory, 2006, and Journal of Computational Finance, 9(4):89-112, 2006. In fact, I still have oscillations with the Rannacher method 1/4 from this article, so I will move to your method (Lawson-Morris).
 
User avatar
SemiMartingale
Topic Author
Posts: 0
Joined: March 18th, 2008, 10:40 am

finite element solution

July 8th, 2008, 1:37 pm

Here is the web page to get the file:http://people.maths.ox.ac.uk/~gilesm/finance.htmlThe name of the article is: M.B. Giles and R. Carter. `Convergence analysis of Crank-Nicolson and Rannacher time-marching', Report NA-05/16, Oxford University Computing Laboratory, 2006, and Journal of Computational Finance, 9(4):89-112, 2006. In fact, I still have oscillations with the Rannacher method 1/4 from this article, so I will move to your method (Lawson-Morris).
 
User avatar
SemiMartingale
Topic Author
Posts: 0
Joined: March 18th, 2008, 10:40 am

finite element solution

July 8th, 2008, 1:38 pm

Here is the web page to get the file:http://people.maths.ox.ac.uk/~gilesm/finance.htmlThe name of the article is: M.B. Giles and R. Carter. `Convergence analysis of Crank-Nicolson and Rannacher time-marching', Report NA-05/16, Oxford University Computing Laboratory, 2006, and Journal of Computational Finance, 9(4):89-112, 2006. In fact, I still have oscillations with the Rannacher method 1/4 from this article, so I will move to your method (Lawson-Morris).
 
User avatar
SemiMartingale
Topic Author
Posts: 0
Joined: March 18th, 2008, 10:40 am

finite element solution

July 8th, 2008, 1:43 pm

sorry for the spam, I got a problem with my browser ...
 
User avatar
Cuchulainn
Posts: 20254
Joined: July 16th, 2004, 7:38 am
Location: 20, 000

finite element solution

July 9th, 2008, 12:37 am

QuoteIn fact, I still have oscillations with the Rannacher method 1/4 from this article, so I will move to your method (Lawson-Morris).I think Roelof Sheppard is the one to take the laurels. All I did was to sugget the scheme to him.BTW there are two LM articles, I and II in SIAM jrnl. Thanks for the link.
Last edited by Cuchulainn on July 8th, 2008, 10:00 pm, edited 1 time in total.
 
User avatar
SemiMartingale
Topic Author
Posts: 0
Joined: March 18th, 2008, 10:40 am

finite element solution

July 9th, 2008, 3:30 pm

So the idea is to use a fully implicit scheme (for all time steps) to get L0-stable and then to use second order approximation (LM method) in time and richardson extrapolation to get stable. That's it ?As my initial condition is a dirac , could it be a solution to simply smooth it ? I have seen a post from you Cuchulainn on this subject but I couldn't find it again. Do you have an article with a method to smooth an initial condition ?
 
User avatar
SemiMartingale
Topic Author
Posts: 0
Joined: March 18th, 2008, 10:40 am

finite element solution

July 9th, 2008, 3:31 pm

I meant to increase accuracy for the LM method and the Richardson extrapolation.