A Posteriori Error Bounds for Approximations of the Oseen Problem and Applications to the Uzawa Iteration Algorithm

Abstract

Abstract:We derive computable bounds of deviations from the exact solution of the stationary Oseen problem. They are applied to approximations generated by the Uzawa iteration method. Also, we derive an advanced form of the estimate, which takes into account approximation errors arising due to discretization of the boundary value problem, generated by the main step of the Uzawa method. Numerical tests con rm our theoretical results and show practical applicability of the estimates.

Error Estimates of Uzawa Iteration Method for a Class of Bingham Fluids

“…Now, our goal is to obtain somewhat different forms of these estimates adapted to approximations generated by Uzawa method. Similar estimates have been recently presented in [18] for the Oseen problem.…”

Estimates of the Distance to Exact Solutions of the Stokes Problem with Slip and Leak Boundary Conditions

“…we conclude that v satisfies (1.14). So far the estimate is not fully computable because the term | | | L η,τ | | | contains the supremum over an infinite amount of functions (however, majorants of this type may be useful for other purposes, for example, for analysis of errors in Uzawa type iteration methods [20]).…”

“…For some problems with nonlinear boundary conditions estimates of this type have been earlier obtained in [18,19] by methods of duality theory and convex analysis (which differs from the method used in this paper). In [20], the estimates were used for analysis of approximations generated by the Uzawa method.…”