Quantcast
  • Register
Adv. Query
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Most popular tags

Related questions

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,355 answers , 22,793 comments
1,470 users with positive rep
820 active unimported users
More ...

  Numerical Analysis of Elliptic PDEs

+ 12 like - 0 dislike
1581 views

I am looking for an elementary reference regarding issues of stability in numerical analysis of non-linear elliptic PDEs, particularly using the finite difference method (but something more comprehensive, covering more sophisticated methods, is even better). Ideally, something aimed at a physicist or applied math audience would be easiest for me to read, but that is not a strict requirement. To be clear, implementation of the method (using your favourite software or programming language) is not the issue, I am more interested in the mathematics involved in numerical stability.

This post has been migrated from (A51.SE)
asked Dec 3, 2011 in Theoretical Physics by Moshe (2,405 points) [ no revision ]
retagged Mar 18, 2014 by dimension10
This may be a good one for the new scicomp.se private beta. If you think so too, I can invite you.

This post has been migrated from (A51.SE)
commented Dec 4, 2011 by Mark S. Everitt (180 points) [ no revision ]
Thanks Mark, but since this is already posted here, I'd leave it. Certainly the next question I have will go there.

This post has been migrated from (A51.SE)
commented Dec 5, 2011 by Moshe (2,405 points) [ no revision ]
No problem. It just went into open beta, so if you want to ask a question in the future then there's no need for invites.

This post has been migrated from (A51.SE)
commented Dec 7, 2011 by Mark S. Everitt (180 points) [ no revision ]

2 Answers

+ 4 like - 0 dislike

Two collegues of mine wrote a monograph

Faragó, Karátson: Numerical solution of nonlinear elliptic problems

where conditioning and preconditioning are an issue. This may be some help though...

If you want it more elementary, then

Larsson, Thomee

is the best.

Do you have a special equation in mind? That would help.

This post has been migrated from (A51.SE)
answered Dec 3, 2011 by András Bátkai (275 points) [ no revision ]
Thanks, this is more or less what I had in mind.

This post has been migrated from (A51.SE)
commented Dec 5, 2011 by Moshe (2,405 points) [ no revision ]
+ 3 like - 0 dislike

Moshe, do you have access to coursework at the University of Idaho? They have a course listing that has your question in the title of the course.

Math WS547 Numerical Analysis of Elliptic PDE's (3 cr) WSU Math 546

However, they don't seem to describe the course itself beyond that.

I did find this paper entitled: LECTURES on COMPUTATIONAL NUMERICAL ANALYSIS of PARTIAL DIFFERENTIAL EQUATIONS (PDF) that may be more in line with what you are looking for (specifically chapter 2).

As for software, MUDPACK is one that I managed to find.

Hope that helps.

This post has been migrated from (A51.SE)
answered Dec 3, 2011 by Larian LeQuella (110 points) [ no revision ]
Thanks for your help.

This post has been migrated from (A51.SE)
commented Dec 5, 2011 by Moshe (2,405 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ys$\varnothing$csOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification
 | OverSnow Theme by polarkernel and dimension10, based on Snow Theme by Q2A Market
Powered by Question2Answer




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...