Rodolfo Araya, Cristian Cárcamo, Abner Poza, Frederic Valentin:
An adaptative multiscale hybrid-mixed method for the Oseen equations
A novel residual a posteriori error estimator for the Oseen equations achieves efficiency and reliability by including multi-level contributions in its construction. Originates from the Multiscale Hybrid Mixed (MHM) method, the estimator combines residuals from the skeleton of the first-level partition of the domain, along with the contributions from element-wise approximations. The second-level estimator is local and infers the accuracy of multiscale basis computations as part of the MHM framework. Also, the face-degrees of freedom of the MHM method shape the estimator and induce a new face-adaptive procedure on the mesh’s skeleton only. As a result, the approach avoids re-meshing the first-level partition, which makes the adaptive process affordable and straightforward on complex geometries. Several numerical tests assess theoretical results.