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.

http://hdl.handle.net/10400.2/9684

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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.