A projection method based on self-adaptive rules for Stokes equations with nonlinear slip boundary conditions

Abstract

In this work we propose and study a self-adaptive projection method for the numerical solution of Stokes equations under slip boundary conditions. We introduce the projection operator to formulate the slip constraint as a fixed point equation. To solve this problem we suggest a projection method by reformulating the nonlinear slip boundary conditions into an iterative form. To make the method more efficient, we find a self-adaptive rule that uses iterative functions to adjust the penalty parameter automatically. We show the convergence of the method in function space and give its application in detail. Finally, the numerical results are given to support our theoretical results.