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

2010/12/22 by Takahito Kashiwabara, Kashiwabara, Takahito
Computer Science · Engineering · #35J87 #35Q30 #65N30 #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1012.4982

openalex publication_date 2010/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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