Analysis of an adaptive Uzawa finite element method for the nonlinear Stokes problem

A Convergent Adaptive Uzawa Finite Element Method for the Nonlinear Stokes Problem

An Optimal Adaptive Finite Element Method for the Stokes Problem

A new adaptive finite element method for solving the Stokes equations is developed, which is shown to converge with the best possible rate. The method consists of 3 nested loops. The outermost loop consists of an adaptive finite element method for solving the pressure from the (elliptic) Schur complement system that arises by eliminating the velocity. Each of the arising finite element problems...

Adaptive Finite Element Algorithms for the Stokes Problem: Convergence Rates and Optimal Computational Complexity

Although adaptive finite element methods (FEMs) are recognized as powerful techniques for solving mixed variational problems of fluid mechanics, usually they are not even proven to converge. Only recently, in [SINUM, 40 (2002), pp.1207-1229] Bänsch, Morin and Nochetto introduced an adaptive Uzawa FEM for solving the Stokes problem, and showed its convergence. In their paper, numerical experimen...

An Adaptive Uzawa FEM for the Stokes Problem: Convergence without the Inf-Sup Condition

We introduce and study an adaptive finite element method (FEM) for the Stokes system based on an Uzawa outer iteration to update the pressure and an elliptic adaptive inner iteration for velocity. We show linear convergence in terms of the outer iteration counter for the pairs of spaces consisting of continuous finite elements of degree k for velocity, whereas for pressure the elements can be e...

On a Finite Element Approximation of the Stokes Problem under Leak or Slip Boundary Conditions of Friction Type

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. Se...