Solving boundary value problems on manifolds with a plane waves method

Carlos J. S. Alves, Nuno F. M. Martins, Svilen S. Valtchev, Pedro R. S. Antunes

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper we consider a plane waves method as a numerical technique for solving boundary value problems for linear partial differential equations on manifolds. In particular, the method is applied to the Helmholtz–Beltrami equations. We prove density results that justify the completeness of the plane waves space and justify the approximation of domain and boundary data. A-posteriori error estimates and numerical experiments show that this simple technique may be used to accurately solve boundary value problems on manifolds.

Original languageEnglish
Article number106426
JournalApplied Mathematics Letters
Publication statusPublished - Sept 2020


  • Helmholtz–Beltrami operator
  • Manifolds
  • Meshfree method
  • Plane waves method


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