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- Title
REDUCED BASIS METHOD FOR PARAMETRIZED ELLIPTIC ADVECTION REACTION PROBLEMS.
- Authors
Dedè, Luca
- Abstract
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.
- Subjects
PARTIAL differential equations; FINITE element method; ERRORS; APPROXIMATION theory; NUMERICAL analysis
- Publication
Journal of Computational Mathematics, 2010, Vol 28, Issue 1, p122
- ISSN
0254-9409
- Publication type
Article
- DOI
10.4208/jcm.2009.09-m3015