An improved error bound for reduced basis approximation of linear parabolic problems
نویسندگان
چکیده
منابع مشابه
An improved error bound for reduced basis approximation of linear parabolic problems
We consider a space-time variational formulation for linear parabolic partial differential equations. We introduce an associated Petrov-Galerkin truth finite element discretization with favorable discrete inf-sup constant βδ, the inverse of which enters into error estimates: βδ is unity for the heat equation; βδ decreases only linearly in time for non-coercive (but asymptotically stable) convec...
متن کاملA new error bound for Reduced Basis approximation of parabolic partial differential equations
We consider a space-time variational formulation for linear parabolic partial differential equations. We introduce an associated Petrov-Galerkin truth finite element discretization with favorable discrete inf-sup constant βδ: βδ is bounded from below by unity for the heat equation; βδ grows only linearly in time for non-coercive (asymptotically stable) convection operators. The latter in turn p...
متن کاملReduced-basis output bound methods for parabolic problems
In this paper, we extend reduced-basis output bound methods developed earlier for elliptic problems, to problems described by parametrized parabolic partial differential equations. The essential new ingredient and the novelty of this paper consist in the presence of time in the formulation and solution of the problem. First, without assuming a time discretization, a reduced-basis procedure is p...
متن کاملAn improved error bound for linear complementarity problems for B-matrices
A new error bound for the linear complementarity problem when the matrix involved is a B-matrix is presented, which improves the corresponding result in (Li et al. in Electron. J. Linear Algebra 31(1):476-484, 2016). In addition some sufficient conditions such that the new bound is sharper than that in (García-Esnaola and Peña in Appl. Math. Lett. 22(7):1071-1075, 2009) are provided.
متن کاملThe Static Condensation Reduced Basis Element Method for Parabolic Problems
We present a new approach for fast, flexible and reliable simulations of parameterdependent parabolic problems with a component-based geometry. The static condensation reduced basis element (SCRBE) is a domain decomposition method with reduced basis (RB) approximation at the intradomain level to populate a Schur complement at the interdomain level. In the Offline stage, for a library of archety...
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: Mathematics of Computation
سال: 2013
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2013-02782-2