A novel L∞L∞ analysis for finite volume approximations of the Stokes problem

In this paper, a novel L∞L∞ analysis for finite volume approximations of the Stokes problem is presented. Optimal order estimates in the L∞L∞-norm for the velocity gradient and pressure of this problem are obtained by using new technical results. In particular, these optimal error estimates for the finite volume approximations are obtained without the presence of a usual logarithmic factor O(|logh|)O(|logh|) for the stationary Stokes problem. Several numerical tests are performed to check these theoretical expectations.