Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Numerical Analysis

arXiv:0708.0025 (math)
[Submitted on 31 Jul 2007]

Title:Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation

Authors:Marcel Arndt, Mitchell Luskin
View PDF
Abstract: We give a goal-oriented a posteriori error estimator for the atomistic-continuum modeling error in the quasicontinuum method, and we use this estimator to design an adaptive algorithm to compute a quantity of interest to a given tolerance by using a nearly minimal number of atomistic degrees of freedom. We present computational results that demonstrate the effectiveness of our algorithm for a periodic array of dislocations described by a Frenkel-Kontorova type model.
Comments: 9 pages, 2 figures
Subjects: Numerical Analysis (math.NA); Mathematical Physics (math-ph)
MSC classes: 65Z05, 70C20, 70G75
Cite as: arXiv:0708.0025 [math.NA]
  (or arXiv:0708.0025v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.0708.0025

Submission history

From: Marcel Arndt [view email]
[v1] Tue, 31 Jul 2007 21:01:17 UTC (24 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.NA
< prev   |   next >
new | recent | 2007-08
Change to browse by:
math
math-ph
math.MP

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)