Details

Autor(en) / Beteiligte

• Ganesan, Sashikumaar
• Matthies, Gunar
• Tobiska, Lutz

Titel

Local projection stabilization of equal order interpolation applied to the Stokes problem

Ist Teil von

• Mathematics of computation, 2008-10, Vol.77 (264), p.2039-2060

Ort / Verlag

Providence, RI: American Mathematical Society

Erscheinungsjahr

2008

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The local projection stabilization allows us to circumvent the Babuska--Brezzi condition and to use equal order interpolation for discretizing the Stokes problem. The projection is usually done in a two-level approach by projecting the pressure gradient onto a discontinuous finite element space living on a patch of elements. We propose a new local projection stabilization method based on (possibly) enriched finite element spaces and discontinuous projection spaces defined on the same mesh. Optimal order of convergence is shown for pairs of approximation and projection spaces satisfying a certain inf-sup condition. Examples are enriched simplicial finite elements and standard quadrilateral/hexahedral elements. The new approach overcomes the problem of an increasing discretization stencil and, thus, is simple to implement in existing computer codes. Numerical tests confirm the theoretical convergence results which are robust with respect to the user-chosen stabilization parameter.