Grad-div stabilized discretizations on S-type meshes for the Oseen problem

Research output: Contribution to journalResearch articleContributedpeer-review

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 Qk × Qk1 and Qk × Pkdisc1, k ≥ 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.

Details

Original languageEnglish
Pages (from-to)299-329
Number of pages31
JournalIMA journal of numerical analysis
Volume38
Issue number1
Publication statusPublished - 1 Jan 2018
Peer-reviewedYes

External IDs

ORCID /0000-0002-2458-1597/work/142239732

Keywords

Keywords

  • Grad-div stabilization, Layer-adapted meshes, Oseen equations, Singular perturbations