On a finite element approximation of the Stokes problem under leak or slip boundary conditions of friction type

Details On a finite element approximation of the Stokes problem under leak or slip boundary conditions of friction type On a finite element approximation of the Stokes problem under leak or slip boundary conditions of friction type

2010-12-22

arxiv.org/abs/1012.4982v1

Mathematics

Numerical Analysis

33 pages

Scientific paper

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.

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