Inf-sup conditions for twofold saddle point problems
نویسندگان
چکیده
Necessary and sufficient conditions for existence and uniqueness of solutions are developed for twofold saddle point problems which arise in mixed formulations of problems in continuum mechanics. This work extends the classical saddle point theory to accommodate nonlinear constitutive relations and the twofold saddle structure. Application to problems in incompressible fluid mechanics employing symmetric tensor finite elements for the stress approximation is presented.
منابع مشابه
An Optimal Preconditioner for a Class of Saddle Point Problems with a Penalty Term, Part Ii: General Theory
Iterative methods are considered for saddle point problems with a penalty term. A positive deenite preconditioner is constructed and it is proved that the condition number of the preconditioned system can be made independent of the discretization and the penalty parameters. Examples include the pure displacement problem in linear elasticity, the Timoshenko beam, and the Mindlin-Reissner plate. ...
متن کاملContractive Dual Methods for Incentive Problems
Several recent papers have proposed recursive Lagrangian-basedmethods for solving dynamic contracting problems. Thesemethods give rise to Bellman operators that incorporate either a dual inf-sup or a saddle point operation. We give conditions that ensure the Bellman operator implied by a dual recursive formulation is contractive. JEL codes: C61, C73, D82, E61.
متن کاملObservations on degenerate saddle point problems
We investigate degenerate saddle point problems, which can be viewed as limit cases of standard mixed formulations of symmetric problems with large jumps in coefficients. We prove that they are well-posed in a standard norm despite the degeneracy. By wellposedness we mean a stable dependence of the solution on the right-hand side. A known approach of splitting the saddle point problem into sepa...
متن کاملAnalysis of Preconditioners for Saddle-Point Problems
Analysis of pre onditioners for saddle-point problems D. Loghin and A. J. Wathen Mixed nite element formulations give rise to large, sparse, blo k linear systems of equations the solution of whi h is often sought via a pre onditioned iterative te hnique. In this work we present a general analysis of blo kpre onditioners based on the stability onditions inherited from the formulation of the nite...
متن کاملStability estimates and structural spectral properties of saddle point problems
For a general class of saddle point problems sharp estimates for Babuška’s inf-sup stability constants are derived in terms of the constants in Brezzi’s theory. In the finite-dimensional Hermitian case more detailed spectral properties of preconditioned saddle point matrices are presented, which are helpful for the convergence analysis of common Krylov subspace methods. The theoretical results ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Numerische Mathematik
دوره 118 شماره
صفحات -
تاریخ انتشار 2011