2021/12/23 by Saumya Bajpai, Bajpai, Saumya, Deepjyoti Goswami +3
Engineering · #35Q30 #65M60 #76D05 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2112.12414
openalex publication_date 2021/12/23 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
In this paper, we apply discontinuous finite element Galerkin method to the time-dependent 2D incompressible Navier-Stokes model. We derive optimal error estimates in L^∞(L2)-norm for the velocity and in L^∞(L2)-norm for the pressure with the initial data u0∈ H01∩ H2 and the source function f in L^∞(L2) space. These estimates are established with the help of a new L2-projection and modified Stokes operator on appropriate broken Sobolev space and with standard parabolic or elliptic duality arguments. Estimates are shown to be uniform under the smallness assumption on data. Then, a completely discrete scheme based on the backward Euler method is analyzed, and fully discrete error estimates are derived. We would like to highlight here that the estiablished semi-discrete error estimates related to the L^∞(L2)-norm of velocity and L^∞(L2)-norm of pressure are optimal and sharper than those derived in the earlier articles. Finally, numerical examples validate our theoretical findings.