Grad-div stabilized discretizations on S-type meshes for the Oseen problem. (27th March 2017)

• Record Type: Journal Article
• Authors: Franz, Sebastian; Höhne, Katharina; Matthies, Gunar
• Is Part Of: IMA journal of numerical analysis. Volume 38:Number 1(2018)
• Page Start: 299
• Page End: 329
• Publication Date: 2017-03-27
• Subjects: Oseen equations -- layer-adapted meshes -- singular perturbations -- grad-div stabilization.; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drw069
• Languages: English
• ISSNs: 0272-4979

Abstract

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 $Q_k\times Q_{k-1}$ and $Q_k\times P_{k-1}^{\text{disc}}$, $k\ge 2$, 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.