Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

We analyze a least-squares strong-form kernel collocation formulation for solving second-order elliptic PDEs on smooth, connected, and compact surfaces with bounded geometry. The methods do not require any partial derivatives of surface normal vectors or metric. Based on some standard smoothness assumptions for high-order convergence, we provide the sufficient denseness conditions on the collocation points to ensure the methods are convergent. In addition to some convergence verifications, we also simulate some reaction-diffusion equations to exhibit the pattern formations.

Keywords

mesh-free method, Kansa method, radial basis function, overdetermined collocation, narrowband method

Publication Date

2-2018

Source Publication Title

SIAM Journal on Numerical Analysis

Volume

40

Issue

1

Start Page

A266

End Page

A287

Publisher

Society for Industrial and Applied Mathematics

Peer Reviewed

1

Copyright

Copyright © 2018, Society for Industrial and Applied Mathematics

Funder

This work was partially supported by a Hong Kong Research Grant Council GRF Grant, a Hong Kong Baptist University FRG Grant, and the National Natural Science Foundation of China (11528205).

DOI

10.1137/16M1080410

Link to Publisher's Edition

http://dx.doi.org/10.1137/16M1080410

ISSN (print)

00361429

ISSN (electronic)

10957170

Included in

Mathematics Commons

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