Kernel-Based Meshless Collocation Methods for Solving Coupled Bulk–Surface Partial Differential Equations

Meng Chen*, Leevan LING

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)375-391
Number of pages17
JournalJournal of Scientific Computing
Volume81
Issue number1
DOIs
Publication statusPublished - 1 Oct 2019

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

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

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