Augmented Galerkin Schemes for the Numerical Solution of Scattering by Small Obstacles

Xavier Claeys (1) , Francis Collino (1)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

We are interested in the problem of a bidimensional acoustic wave propagation in a medium including a small obstacle with homogeneous Dirichlet boundary condition. We present and analyse a numerical scheme suitable for finite elements that does not suffer from numerical locking, and takes the presence of the small obstacle into account. It is based on the fictitious domain method combined with matched asymptotic expansions.

Xavier Claeys, Francis Collino. Augmented Galerkin Schemes for the Numerical Solution of Scattering by Small Obstacles. Numerische Mathematik, 2007, 116 (2), pp.243-268. ⟨10.1007/s00211-010-0301-z⟩. ⟨hal-00976812⟩