Alves, Carlos J. S.Antunes, Pedro R. S.Martins, Nuno F. M.Valtchev, Svilen S.2025-09-162025-09-162020-09Carlos J.S. Alves, Pedro R.S. Antunes, Nuno F.M. Martins, Svilen S. Valtchev, Solving boundary value problems on manifolds with a plane waves method, Applied Mathematics Letters, Volume 107, 2020, 106426, ISSN 0893-9659, https://doi.org/10.1016/j.aml.2020.106426.0893-9659http://hdl.handle.net/10400.8/14079In 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.engMeshfree methodPlane waves methodHelmholtz–Beltrami operatorManifoldsjournal article10.1016/j.aml.2020.106426