Abstract

We propose and analyze an unfitted method for a dual-dual mixed formulation of a class of Stokes models with variable viscosity depending on the velocity gradient, in which the pseudoestress, the velocity and its gradient are the main unknowns. On a fluid domain Omega with curved boundary Gwe consider a Dirichlet boundary condition and employ an approach previously applied to the Stokes equations with constant viscosity, which consists of approximating Omega by a polyhedral computational subdomain Omega(h), not necessarily fitting Omega, where a Galerkin method is applied to compute solution. Furthermore, to approximate the Dirichlet data on the computational boundary G (h), we make use of a transferring technique based on integrating the discrete velocity gradient. Then the associated Galerkin scheme can be defined by employing Raviart-Thomas of order k >= 0 for the pseudostress, and discontinuous polynomials of degree kappa for the velocity and its gradient. For the a priorierror analysis we provide suitable assumptions on the mesh near the boundary Gensuring that the associated Galerkin scheme is well-posed and optimally convergent with.( h(kappa+1)). Next, for the case when G h is taken as a piecewise linear interpolation of G, we develop a reliable and quasi-efficient residual-based a posteriorierror estimator. Numerical experiments verify our analysis and illustrate the performance of the associated a posteriorierror indicator.