Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

A meshless kernel-based method is developed to solve coupled second-order elliptic PDEs in bulk domains and surfaces, subject to Robin boundary conditions. It combines a least-squares kernel collocation method with a surface-type intrinsic approach. Therefore, we can use each pair for discrete point sets, RBF kernels (globally and restrictedly), trial spaces, and some essential assumptions, for the search of least-squares solutions in bulks and on surfaces respectively. We first give error estimates for domain-type Robin-boundary problems. Based on this and existing results for surface PDEs, we discuss the theoretical requirements for the employed Sobolev kernels. Then, we select the orders of smoothness for the kernels in bulks and on surfaces. Lastly, several numerical experiments are demonstrated to test the robustness of the coupled method for accuracy and convergence rates under different settings.

Keywords

Meshless collocation methods, Coupled bulk–surface PDEs, Smoothness orders of global and restricted kernels, Error estimate

Publication Date

10-2019

Source Publication Title

Journal of Scientific Computing

Volume

81

Issue

1

Start Page

375

End Page

391

Publisher

Springer

DOI

10.1007/s10915-019-01020-2

Link to Publisher's Edition

https://doi.org/10.1007/s10915-019-01020-2

ISSN (print)

08857474

ISSN (electronic)

15737691

Available for download on Sunday, November 01, 2020

Included in

Mathematics Commons

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