A Kernel-Based Least-Squares Collocation Method for Surface Diffusion

Meng Chen, Ka Chun Cheung, Leevan Ling*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)

Abstract

There are plenty of applications and analyses for time-independent elliptic partial differential equations in the literature hinting at the benefits of overtesting by using more collocation conditions than the number of basis functions. Overtesting not only reduces the problem size, but is also known to be necessary for stability and convergence of widely used asymmetric Kansa-type strong-form collocation methods. We consider kernel-based meshfree methods, which are methods of lines with collocation and overtesting spatially, for solving parabolic partial differential equations on surfaces without parametrization. In this paper, we extend the time-independent convergence theories for overtesting techniques to the parabolic equations on smooth and closed surfaces.
Original languageEnglish
Pages (from-to)1386-1404
Number of pages19
JournalSIAM Journal on Numerical Analysis
Volume61
Issue number3
DOIs
Publication statusPublished - Jun 2023

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics
  • Numerical Analysis

User-Defined Keywords

  • meshfree method
  • Kansa method
  • radial basis function
  • method of lines
  • parabolic PDEs
  • convergence analysis

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