Edge stabilization for the generalized Stokes problem: A continuous interior penalty method

• In this note we introduce and analyze a stabilized finite element method for the generalized Stokes equation. Stabilityis obtained by adding a least squares penalization of the gradient jumps across element boundaries. The method can beseen as a higher order version of the BrezziPitkäranta penalty stabilization [F. Brezzi, J. Pitkäranta, On the stabilizationof finite element approximations of the Stokes equations, in: W. Hackbusch (Ed.), Efficient Solution of EllipticSystems, Vieweg, 1984], but gives better resolution on the boundary for the Stokes equation than does classical Galerkinleast-squares formulation. We prove optimal and quasi-optimal convergence properties for Stokes problem and forthe porous media models of Darcy and Brinkman. Some numerical examples are given.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Strömningsmekanik och akustik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Fluid Mechanics and Acoustics (hsv//eng)

Nyckelord

Inf-sup condition

Stabilized methods

Gradient jumps

Interior penalty method

Finite element

Generalized Stokes equation

Publikations- och innehållstyp

art (ämneskategori)

ref (ämneskategori)