An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations

Comptes Rendus Mathematique - Tập 339 - Trang 667-672 - 2004
Maxime Barrault1, Yvon Maday2, Ngoc Cuong Nguyen3, Anthony T. Patera4
1CERMICS – ENPC, cité Descartes, Champs sur Marne, 77455 Marne la Vallée cedex 2, France
2Laboratoire J.-L. Lions, université Pierre et Marie Curie, B.C. 187, 75242 Paris cedex 05, France
3National University of Singapore, 10 Kent Ridge Crescent, Singapore 117576
4Massachusetts Institute of Technology, Department of Mechanical Engineering, Room 3-264, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA

Tài liệu tham khảo

Almroth, 1978, Automatic choice of global shape functions in structural analysis, AIAA J., 16, 525, 10.2514/3.7539 Fink, 1983, On the error behavior of the reduced basis technique for nonlinear finite element approximations, Z. Angew. Math. Mech., 63, 21, 10.1002/zamm.19830630105 Machiels, 2000, Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems, C. R. Acad. Sci. Paris, Ser. I, 331, 153, 10.1016/S0764-4442(00)00270-6 Maday, 2002, Global a priori convergence theory for reduced-basis approximation of single-parameter symmetric coercive elliptic partial differential equations, C. R. Acad. Sci. Paris, Ser. I, 335, 289, 10.1016/S1631-073X(02)02466-4 Noor, 1980, Reduced basis technique for nonlinear analysis of structures, AIAA J., 18, 455, 10.2514/3.50778 Prud'homme, 2002, Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods, J. Fluids Engrg., 124, 70, 10.1115/1.1448332 Quarteroni, 1991, Numer. Math., vol. 37 Veroy, 2003, A Posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations