A smooth fictitious domain/multiresolution method for elliptic equations on general domains

Ping Yin (1) , Jacques Liandrat (2)

1 JiangNan University
2 I2M - Institut de Mathématiques de Marseille

We propose a smooth fictitious domain/multiresolution method for enhancing the accuracy order in solving second order elliptic partial differential equations on general bivariate domains. We prove the existence and uniqueness of the solution of corresponding discrete problem and the interior error estimate which justifies the improved accuracy order. Numerical experiments are conducted on a cassini oval.

Mots clés: Elliptic partial differential equations; Smooth fictitious domain methods; Multiresolution discretization; Interior error estimate

Domaines: Modélisation et simulation

Ping Yin, Jacques Liandrat. A smooth fictitious domain/multiresolution method for elliptic equations on general domains. Numerical Algorithms, 2016, ⟨10.1007/s11075-015-0063-x⟩. ⟨hal-01266859⟩