On a finite element approximation of the Stokes problem under leak or slip boundary conditions of friction type
Provides a rigorous numerical framework for a specific nonlinear boundary condition in fluid dynamics, but the contribution is incremental as it extends existing methods to a particular problem class.
The paper develops a finite element approximation for Stokes equations with nonlinear slip/leak boundary conditions of friction type, proving existence, uniqueness, and error estimates, with numerical examples validating the theory.
A finite element approximation of the Stokes equations under a certain nonlinear boundary condition, namely, the slip or leak boundary condition of friction type, is considered. We propose an approximate problem formulated by a variational inequality, prove an existence and uniqueness result, present an error estimate, and discuss a numerical realization using an iterative Uzawa-type method. Several numerical examples are provided to support our theoretical results.