A Kernel-Based Embedding Method and Convergence Analysis for Surfaces PDEs

Ka Chun Cheung, Leevan Ling*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

27 Citations (Scopus)
35 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)A266-A287
Number of pages22
JournalSIAM Journal on Scientific Computing
Issue number1
Publication statusPublished - 6 Feb 2018

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Kansa method
  • Mesh-free method
  • Narrowband method
  • Overdetermined collocation
  • Radial basis function


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