A second order in time local projection stabilized Lagrange–Galerkin method for Navier–Stokes equations at high Reynolds numbers. (August 2016)

• Record Type: Journal Article
• Authors: Bermejo, R.; Saavedra, L.
• Is Part Of: Computers & mathematics with applications. Volume 72:issue 4(2016)
• Page Start: 820
• Page End: 845
• Publication Date: 2016-08
• Subjects: Lagrange–Galerkin -- Finite elements -- Local projection stabilization -- High Reynolds numbers -- Navier–Stokes; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.05.012
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We present a stabilized Backward Difference Formula of order 2-Lagrange Galerkin method to integrate the incompressible Navier–Stokes equations at high Reynolds numbers (Re). The stabilization of the conventional Lagrange–Galerkin method is done via a local projection technique for inf–sup stable finite elements. We prove that for a finite time T the a priori error estimate for velocity in a mesh dependent norm is O ( h m + Δ t 2 ), whereas the error for pressure in the l 2 ( L 2 ( D ) ) norm is O ( h m + Δ t 2 ), with error constants that are independent of the Re − 1 ; here, m denotes the degree of the polynomials of the velocity finite element space. The size of the stabilization parameters is calculated from the velocity error estimate in a way that the error is optimal when the solution is sufficiently smooth. Numerical examples at high Reynolds numbers show the robustness of our method.