Solving boundary value problems on manifolds with a plane waves method
Alves, Carlos J. S.; Antunes, Pedro R. S.; Martins, Nuno F. M.; Valtchev, Svilen S.
Applied Mathematics Letters, 107 (2020), 106426
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.