(Springer Science+Business Media, LLC (Springer Nature), 2019-08-15) Frutos, Javier de; García-Archilla, Bosco; Novo, Julia; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Economía. España; Agencia Española de Investigación; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Junta de Castilla-León; Universidad de Sevilla. TIC130: Investigación en Sistemas DInámicos en Ingeniería
This paper studies fully discrete approximations to the evolutionary Navier–Stokes equations by means of inf-sup stable H1-conforming mixed finite elements with a grad-div type stabilization and the Euler incremental projection method in time. We get error bounds where the constants do not depend on negative powers of the viscosity. We get the optimal rate of convergence in time of the projection method. For the spatial error we get a bound O(hk) for the L2 error of the velocity, k being the degree of the polynomials in the velocity approximation. We prove numerically that this bound is sharp for this method.
