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:1812.08323 (math)
[Submitted on 18 Dec 2018 (v1), last revised 9 May 2020 (this version, v3)]

Title:Isogeometric Collocation Method for the Fractional Laplacian in the 2D Bounded Domain

Authors:Kailai Xu, Eric Darve
View PDF
Abstract:We consider the isogeometric analysis for fractional PDEs involving the fractional Laplacian in two dimensions. An isogeometric collocation method is developed to discretize the fractional Laplacian and applied to the fractional Poisson problem and the time-dependent fractional porous media equation. Numerical studies exhibit monotonous convergence with a rate of $\mathcal{O}(N^{-1})$, where $N$ is the degrees of freedom. A comparison with finite element analysis shows that the method enjoys higher accuracy per degree of freedom and has a better convergence rate. We demonstrate that isogeometric analysis offers a novel and promising computational tool for nonlocal problems.
Comments: 23 pages, 8 figures
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1812.08323 [math.NA]
  (or arXiv:1812.08323v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1812.08323

Submission history

From: Kailai Xu [view email]
[v1] Tue, 18 Dec 2018 17:59:21 UTC (7,215 KB)
[v2] Sun, 26 May 2019 22:43:15 UTC (4,967 KB)
[v3] Sat, 9 May 2020 07:10:33 UTC (4,964 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.NA
< prev   |   next >
new | recent | 2018-12
Change to browse by:
cs
cs.NA
math

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?)