A staggered finite volume scheme on general meshes for the generalized Stokes problem in two space dimensions AstaggeredschemefortheStokesequations

International audienceThis paper presents a new finite volume scheme for the steady Stokes equations on a general 2D mesh. The scheme is staggered, i.e. thediscrete velocities are not located at the same place as the discrete pressures. We prove the existence and the uniqueness of a discretesolution. We then prove convergence of the discrete velocities to theweak solution of the problem. Under additional regularity conditions,we prove the convergence of a penalized version of the scheme to the weak solution of the problem. Numerical experiments on problems withknown analytical solutions allow to obtain the rate of convergence for both velocities and pressur