Conditions for superconvergence of HDG methods for stokes flow

Bernardo Cockburn, Ke Shi

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

We provide an a priori error analysis of a wide class of finite element methods for the Stokes equations. The methods are based on the velocity gradient-velocity-pressure formulation of the equations and include new and old mixed and hybridizable discontinuous Galerkin methods. We show how to reduce the error analysis to the verification of some properties of an elementwise-defined projection and of the local spaces defining the methods. We also show that the projection of the errors only depends on the approximation properties of the projection. We then provide sufficient conditions for the superconvergence of the projection of the error in the approximate velocity. We give many examples of these methods and show how to systematically construct them from similar methods for the diffusion equation.

Original languageEnglish (US)
Pages (from-to)651-671
Number of pages21
JournalMathematics of Computation
Volume82
Issue number282
DOIs
StatePublished - 2013

Fingerprint Dive into the research topics of 'Conditions for superconvergence of HDG methods for stokes flow'. Together they form a unique fingerprint.

Cite this