REDUCED BASIS METHOD FOR PARAMETRIZED ELLIPTIC ADVECTION-REACTION PROBLEMS

作     者：Luca Dedè 

作者机构：MOX-Modeling■Scientific ComputingDipartimento di Matematica"F.Brioschi"Politecnico di Milano 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2010年第28卷第1期

页      面：122-148页

核心收录：

学科分类：081702[工学-化学工艺] 07[理学] 08[工学] 0817[工学-化学工程与技术] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：support provided thorough the "Progetto Rocca"  MIT-Politecnico di Milano collaboration 

主　　题：Parametrized advection-reaction partial differential equations Reduced Basis method "primal-dual" reduced basis approach Stabilized finite element method a posteriori error estimation. 

摘      要：In this work we consider the Reduced Basis method for the solution of parametrized advection-reaction partial differential equations. For the generation of the basis we adopt a stabilized finite element method and we define the Reduced Basis method in the ＂primal- dual＂ formulation for this stabilized problem. We provide a priori Reduced Basis error estimates and we discuss the effects of the finite element approximation on the Reduced Basis error. We propose an adaptive algorithm, based on the a posteriori Reduced Basis error estimate, for the selection of the sample sets upon which the basis are built; the idea leading this algorithm is the minimization of the computational costs associated with the solution of the Reduced Basis problem. Numerical tests demonstrate the efficiency, in terms of computational costs, of the ＂primal-dual＂ Reduced Basis approach with respect to an ＂only primal＂ one. Parametrized advection-reaction partial differential equations, Reduced Basis method, ＂primal-dual＂ reduced basis approach, Stabilized finite element method, a posteriori error estimation.