Mathematics

Discontinuous viscosities are of interest in many applications. Classical adaptive numerical methods perform under the restricting assumption that the discontinuities of the viscosity are captured by the initial partition. This excludes applications where the jump of the viscosity takes place across curves, manifolds or at a priori unknown positions. Based on a novel perturbation theory, we introduce an adaptive nite element method which approximates the solution of Stokes equations with possible discontinuous viscosities. It is based on known routines used to approximate the viscosity and the solution of the Stokes problem when the discontinuities are aligned with the input mesh. A result showing the quasi-optimality of this method is introduced and numerical results are presented.