Rodolfo Araya, Gabriel R. Barrenechea, Abner Poza, Frederic Valentin:
Convergence analysis of a residual local projection finite element method for the Navier-Stokes equations
This work presents and analyzes a new Residual Local Projection stabilized finite element method (RELP) for the non-linear incompressible Navier-Stokes equations. Stokes problems defined element-wisely drive the construction of the residual-based terms which make the present method stable for the finite element pairs P1/Pl, l=0,1. Numerical upwinding is incorporated through an extra control on the advective derivative and on the residual of the divergence equation. Existence of the discrete solution and uniqueness of a non-singular branch of solutions, as well as optimal error estimates in natural norms are proved under standard assumptions. Next, a divergence-free velocity field is provided by a simple post-processing of the computed velocity and pressure using the lowest order Raviart-Thomas basis functions. This updated velocity is proved to converge optimally to the exact solution. Numerics asses the theoretical results and validate the RELP method.
Esta prepublicacion dio origen a la(s) siguiente(s) publicación(es) definitiva(s):
Rodolfo ARAYA, Gabriel R. BARRENECHEA, Abner POZA, Frederic VALENTIN: Convergence analysis of a residual local projection finite element method for the Navier-Stokes equations. SIAM Journal on Numerical Analysis, vol. 50, 2, pp. 669-699, (2012).