Main Article Content
Abstract
We analyze Local Projection Stabilization (LPS) methods for the solution of Stokes problem using equal order finite elements. We investigate their convergence, stability and accuracy properties. The resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations. We distinguish two classes of LPS methods: one-level and two-level methods. Numerical examples using bilinear interpolations are presented to validate the analysis and assess the accuracy of both approaches.
Keywords
Article Details
References
- BECKER, R. and BRAACK, M. 2001. A finite element pressure gradient stabilization for the Stokes equations based on local projections, Calcolo 38(4): 173-199.
- BREZZI, F. and FORTIN, M. 1991. Mixed and Hybrid Finite Element Methods, Springer Verlag, New York, USA.
- GANESAN, S., MATTHIES, G. and TOBISKA, L. 2008. Local projection stabilization of equal order interpolation applied to the Stokes problem, Math. Comp., 77: 2039-2060.
- GIRAULT, V. and RAVIART, P.A. 1986. Finite Element Methods for Navier-Stokes Equations, Springer Verlag, Berlin, Germany.
- MATTHIES, G. SKRYPACZ, P., TOBISKA, L. 2007. A unified convergence analysis for local projection stabilisations applied to the Oseen problem, M2AN Math, Model. Numer. Anal., 41(4): 713-742.
- NAFA, K. 2008. Two-level Pressure stabilization method for the generalized Stokes Problem, International Journal of Computer, Mathematics 3-4: 579-585.
- NAFA, K. and WATHEN, A. 2009. Local projection stabilized Galerkin approximations for the generalized Stokes problem, Comput. Methods Appl. Mech. Engrg., 198: 877-883.
References
BECKER, R. and BRAACK, M. 2001. A finite element pressure gradient stabilization for the Stokes equations based on local projections, Calcolo 38(4): 173-199.
BREZZI, F. and FORTIN, M. 1991. Mixed and Hybrid Finite Element Methods, Springer Verlag, New York, USA.
GANESAN, S., MATTHIES, G. and TOBISKA, L. 2008. Local projection stabilization of equal order interpolation applied to the Stokes problem, Math. Comp., 77: 2039-2060.
GIRAULT, V. and RAVIART, P.A. 1986. Finite Element Methods for Navier-Stokes Equations, Springer Verlag, Berlin, Germany.
MATTHIES, G. SKRYPACZ, P., TOBISKA, L. 2007. A unified convergence analysis for local projection stabilisations applied to the Oseen problem, M2AN Math, Model. Numer. Anal., 41(4): 713-742.
NAFA, K. 2008. Two-level Pressure stabilization method for the generalized Stokes Problem, International Journal of Computer, Mathematics 3-4: 579-585.
NAFA, K. and WATHEN, A. 2009. Local projection stabilized Galerkin approximations for the generalized Stokes problem, Comput. Methods Appl. Mech. Engrg., 198: 877-883.