A simple pressure stabilization method for the Stokes equation

• Published in: Communications in numerical methods in engineering Vol. 24; no. 11; pp. 1421 - 1430
• Main Authors: Becker, Roland, Hansbo, Peter
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.11.2008; Wiley; John Wiley and Sons
• Subjects: Beräkningsmatematik; Computational Mathematics; Computational techniques; Engineering Sciences; equal-order interpolation; Exact sciences and technology; Fluid dynamics; Fluid Mechanics; Fundamental areas of phenomenology (including applications); General theory; Mathematical methods in physics; Physics; stabilization; Stokes problem; Strömningsmekanik; Incompressible flow; Stokes problem; Stokes equation; Stabilization; Polynomial approximation; Quadratic approximation; equal-order interpolation; Piecewise linear system; stabilization
• ISSN: 1069-8299; 2040-7939; 1099-0887; 1099-0887; 2040-7947
• DOI: 10.1002/cnm.1041

In this paper, we consider a stabilization method for the Stokes problem, using equal‐order interpolation of the pressure and velocity, which avoids the use of the mesh size parameter in the stabilization term. We show that our approach is stable for equal‐order interpolation in the case of piecewise linear and piecewise quadratic polynomials on triangles. In the case of linear polynomials, we retrieve a well‐known idea of using mass lumping as a stabilization mechanism. Copyright © 2007 John Wiley & Sons, Ltd.