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

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 partial differential equations solutions defined on complex domains. It couples a smooth fictitious domain method derived in Haslinger et al. (Numer Linear Algebra 14:713–739, 2007) with multiscale approximations. After the definition of the method, error estimates 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). Numerical implementation and tests on univariate elliptic problems are finally described.

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