Coupling wavelets/vaguelets and smooth fictitious domain methods for elliptic problems: the univariate case

Ping Yin (1) , Jacques Liandrat (2)

1 Changlin Company
2 I2M - Institut de Mathématiques de Marseille

This work is devoted to the definition, the analysis and the implementation in the univariate case of a new numerical method for the approximation of par-tial differential equations solutions defined on complex domains. It couples a smooth fictitious domain method of Haslinger et al. [Projected Schur com-plement method for solving non-symmetric systems arising from a smooth fictitious domain approach, Numer. Linear Algebra 14(2007) 713-739] with multiscale approximations. After the definition of the method, error esti-mates are derived: they allow to control a global error (on the whole domain including the boundary of the initial complex domain) as well as an interior error (for any sub-domain strictly included in the control domain). Nu-merical implementation and tests on univariate elliptic problems are finally described.

Mots clés: smooth fictitious domain method; elliptic problem; error estimate; multiscale approximation

Domaines: Modélisation et simulation

Ping Yin, Jacques Liandrat. Coupling wavelets/vaguelets and smooth fictitious domain methods for elliptic problems: the univariate case. Computational & Applied Mathematics, 2016, pp.DOI: 10.1007/s40314-014-0136-9. ⟨10.1007/s40314-014-0136-9⟩. ⟨hal-01108936⟩