TY - JOUR
AU1 - García-Archilla, Bosco
AU2 - Novo, Julia
AB - This paper studies fully discrete finite element approximations to the Navier–Stokes equations using inf-sup stable elements and grad-div stabilization. For the time integration, two implicit–explicit second-order backward differentiation formulae (BDF2) schemes are applied. In both, the Laplacian is implicit while the nonlinear term is explicit, in the first one, and semiimplicit, in the second one. The grad-div stabilization allows us to prove error bounds in which the constants are independent of inverse powers of the viscosity. Error bounds of order $r$ in space are obtained for the $L^2$ error of the velocity using piecewise polynomials of degree $r$ to approximate the velocity together with second-order bounds in time, both for fixed time-step methods and for methods with variable time steps. A Courant Friedrichs Lewy (CFL)-type condition is needed for the method in which the nonlinear term is explicit relating time-step and spatial mesh-size parameters.
TI - Robust error bounds for the Navier–Stokes equationsusing implicit-explicit second-order BDF method with variable steps
JF - IMA Journal of Numerical Analysis
DO - 10.1093/imanum/drac058
DA - 2022-10-04
UR - https://www.deepdyve.com/lp/oxford-university-press/robust-error-bounds-for-the-navier-stokes-equationsusing-implicit-60de8ySzp0
SP - 2892
EP - 2933
VL - 43
IS - 5
DP - DeepDyve
ER -