A Reduced Basis Method for Parametrized Variational Inequalities
نویسندگان
چکیده
منابع مشابه
A Reduced Basis Method for Parametrized Variational Inequalities
Reduced basis methods are an efficient tool for significantly reducing the computational complexity of solving parametrized partial differential equations. Originally introduced for elliptic equations, they have been generalized during the last decade to various types of elliptic, parabolic and hyperbolic systems. In this article, we extend the reduction technique to parametrized variational in...
متن کاملReduced Basis Method for Variational Inequalities in Contact Mechanics
We present an efficient model order reduction method [1] for parametrized elliptic variational inequalities of the first kind: find u ∈ K such that: a(u, v − u;μ) ≥ f(v − u;μ), ∀v ∈ K(μ) where K(μ) := {v ∈ H1(Ω)|Bv ≤ g(μ)}. Motivated by numerous engineering applications that involve contact between elastic body and rigid obstacle, e.g. the obstacle problem [2], we develop a primaldual reduced b...
متن کاملReduced Basis Method for Parametrized Elliptic Optimal Control Problems
We propose a suitable model reduction paradigm – the certified reduced basis method (RB) – for the rapid and reliable solution of parametrized optimal control problems governed by partial differential equations (PDEs). In particular, we develop the methodology for parametrized quadratic optimization problems with elliptic equations as constraint. Firstly, we recast the optimal control problem i...
متن کاملAN INTRODUCTION TO REDUCED BASIS METHOD FOR PARAMETRIZED PDEs
We provide an introduction on reduced basis (RB) method for the solution of parametrized partial differential equations (PDEs). We introduce all the main ingredients to describe the methodology and the algorithms used to build the approximation spaces and the error bounds. We consider a model problem describing a steady potential flow around parametrized bodies and we provide some illustrative ...
متن کاملA Certified Reduced Basis Method for Parametrized Elliptic Optimal Control Problems∗
In this paper, we employ the reduced basis method as a surrogate model for the solution of linear-quadratic optimal control problems governed by parametrized elliptic partial differential equations. We present a posteriori error estimation and dual procedures that provide rigorous bounds for the error in several quantities of interest: the optimal control, the cost functional, and general linea...
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: SIAM Journal on Numerical Analysis
سال: 2012
ISSN: 0036-1429,1095-7170
DOI: 10.1137/110835372