A priori and a posteriori estimates of the stabilized finite element methods for the incompressible flow with slip boundary conditions arising in arteriosclerosis

Abstract

In this paper, we develop the lower order stabilized finite element methods for the incompressible flow with the slip boundary conditions of friction type whose weak solution satisfies a variational inequality. The H 1 -norm for the velocity and the L 2 -norm for the pressure decrease with optimal convergence order. The reliable and efficient a posteriori error estimates are also derived. Finally, numerical experiments are presented to validate the theoretical results. MSC: 35L70; 65N30; 76D06

GLS methods for Stokes equations under boundary condition of friction type: formulation-analysis-numerical schemes and simulations

“…The GLS method has been introduced in the early 80's when T. J. R. Hughes and co-workers realized the lack of stability and formulated new methods for advectiondominated diffusion problems and for incompressible flows in [11,12,13,14,15,16,17], and later extended to compressible flows, [18,19]. Stokes or Navier Stokes equations with Tresca's boundary condition has been considered with pressure stabilization in [20,21,22,23,24], but in our knowledge similar study with GLS stabilization has not yet been considered and it is the object of this work. Thus our challenge is to analyse how the added terms will affect the stability, convergence, and the actual computation.…”