Alves, Carlos J. S.Antunes, Pedro R. S.Martins, Nuno F. M.Valtchev, Svilen S.2020-05-112020-05-1120200893-9659http://hdl.handle.net/10400.2/9684In this paper we consider a plane waves method as a numerical technique for solving boundary value problems for linear partial di erential equations on man- ifolds. 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