An a posteriori error estimate for a dual mixed method applied to Stokes system with non-null source terms

Abstract

In this work, we focus our attention in the Stokes flow with nonhomogeneous source terms, formulated in dual mixed form. For the sake of completeness, we begin recalling the corresponding well-posedness at continuous and discrete levels. After that, and with the help of a kind of a quasi-Helmholtz decomposition of functions in H ( d i v ), we develop a residual type a posteriori error analysis, deducing an estimator that is reliable and locally efficient. Finally, we provide numerical experiments, which confirm our theoretical results on the a posteriori error estimator and illustrate the performance of the corresponding adaptive algorithm, supporting its use in practice.