A DISCONTINUOUS GALERKIN TIME-STEPPING SCHEME FOR THE VELOCITY TRACKING PROBLEM

被引：24

作者：

Casas, Eduardo ^{[1
]}

Chrysafinos, Konstantinos ^{[2
]}

机构：

[1] Univ Cantabria, ETSI Ind & Telecomun, Dept Matemat Aplicada & Ciencias Comp, E-39005 Santander, Spain

[2] Natl Tech Univ Athens, Dept Math, Sch Appl Math & Phys Sci, Athens 15780, Greece

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2012年 / 50卷 / 05期

关键词：

evolution Navier-Stokes equations; optimal control; a priori error estimates; discontinuous Galerkin methods; FINITE-ELEMENT METHODS; NAVIER-STOKES FLOWS; PARABOLIC PROBLEMS; NUMERICAL APPROXIMATION; OPTIMALITY CONDITIONS; DISTRIBUTED CONTROL; DISCRETIZATION;

D O I：

10.1137/110829404

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The velocity tracking problem for the evolutionary Navier-Stokes equations in two dimensions is studied. The controls are of distributed type and are submitted to bound constraints. First and second order necessary and sufficient conditions are proved. A fully discrete scheme based on the discontinuous (in time) Galerkin approach, combined with conforming finite element subspaces in space, is proposed and analyzed. Provided that the time and space discretization parameters, tau and h, respectively, satisfy tau <= Ch(2), then L-2 error estimates of order O(h) are proved for the difference between the locally optimal controls and their discrete approximations.

引用

页码：2281 / 2306

页数：26

共 33 条

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[2]

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