Grad-div stabilized discretizations on S-type meshes for the Oseen problem. (27th March 2017) - Franz, Sebastian; Höhne, Katharina; Matthies, Gunar
Abstract: We consider discretizations of the singularly perturbed Oseen equations on properly layer-adapted meshes. Using a suitable solution decomposition, we are able to prove optimal convergence orders in the associated energy norm for grad-div stabilized finite element methods in a general setting. Two families of pairs of discrete function spaces, namely Q_k× Q_k-1 and Q_k× P_k-1^disc, k2, are investigated in detail. The usage of a standard nonstabilized Galerkin method reduces the order by 1 while stabilization outside the layers is enough to regain the full optimal order.