Author(s): Alves, Carlos J. S. ; Antunes, Pedro R. S. ; Martins, Nuno F. M. ; Valtchev, Svilen S.
Date: 2020
Persistent ID: http://hdl.handle.net/10400.2/9684
Origin: Repositório Aberto da Universidade Aberta
Subject(s): Meshfree method; Plane waves method; Helmholtz–Beltrami operator; Manifolds; Meshfree method; Meshfree method; Plane waves method; Plane waves method; Helmholtz–Beltrami operator; Helmholtz–Beltrami operator; Manifolds; Manifolds
In 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.
