Lyapunov-Based Error Bounds for the Reduced-Basis Method
نویسندگان
چکیده
منابع مشابه
Output Error Bounds for the Dirichlet-Neumann Reduced Basis Method
The Dirichlet-Neumann reduced basis method is a model order reduction method for homogeneous domain decomposition of elliptic PDE’s on a-priori known geometries. It is based on an iterative scheme with full offline-online decomposition and rigorous a-posteriori error estimates. We show that the primal-dual framework for non-compliant output quantities can be transferred to this method. The resu...
متن کاملReduced Basis A Posteriori Error Bounds for the Instationary Stokes Equations: A Penalty Approach
We present reduced basis approximations and associated rigorous a posteriori error bounds for the instationary Stokes equations. The proposed method is an extension of the penalty approach introduced in Gerner and Veroy (2011b) to the time-dependent setting: The introduction of a penalty term enables us to develop a posteriori error bounds that do not rely on the expensive calculation of inf-su...
متن کاملReduced Basis a Posteriori Error Bounds for Parametrized Linear–Quadratic Elliptic Optimal Control Problems
We employ the reduced basis method as a surrogate model for the solution of optimal control problems governed by parametrized partial differential equations (PDEs) and develop rigorous a posteriori error bounds for the error in the optimal control and the associated error in the cost functional. The proposed bounds can be efficiently evaluated in an offline-online computational procedure. We pr...
متن کاملA Posteriori Error Bounds for Reduced-basis Approximations of Parametrized Parabolic Partial Differential Equations
In this paper, we extend the reduced-basis methods and associated a posteriori error estimators developed earlier for elliptic partial differential equations to parabolic problems with affine parameter dependence. The essential new ingredient is the presence of time in the formulation and solution of the problem – we shall “simply” treat time as an additional, albeit special, parameter. First, ...
متن کاملReduced basis approximation and error bounds for potential flows in parametrized geometries
In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for potential flows in affinely parametrized geometries. We review the essential ingredients: i) a Galerkin projection onto a lowdimensional space associated with a smooth “parametric manifold” in order to get a dimension reduction; ii) an efficient and effective greedy sampling meth...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IFAC-PapersOnLine
سال: 2016
ISSN: 2405-8963
DOI: 10.1016/j.ifacol.2016.07.409