Quasi-optimal adaptive pseudostress approximation of the Stokes equations

C. Carstensen, D. Gallistl, M. Schedensack

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18 Citations (Scopus)
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The pseudostress-velocity formulation of the stationary Stokes problem allows some quasi-optimal Raviart--Thomas mixed finite element formulation for any polynomial degree. The adaptive algorithm employs standard residual-based explicit a posteriori error estimation from Carstensen, Kim, and Park [SIAM J. Numer. Anal., 49 (2011), pp. 2501--2523] for the lowest-order Raviart--Thomas finite element functions in a simply connected Lipschitz domain. This paper proves optimal convergence rates in terms of the number of unknowns of the adaptive mesh-refining algorithm based on the concept of approximation classes. The proofs use some novel equivalence to first-order nonconforming Crouzeix--Raviart discretization plus a particular Helmholtz decomposition of deviatoric tensors.

Original languageEnglish
Pages (from-to)1715-1734
Number of pages20
JournalSIAM journal on numerical analysis
Issue number3
Publication statusPublished - 2013
Externally publishedYes


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