An ‘empirical interpolation’ method: Application to efficient reduced-basis discretization of partial differential equations. (English. Abridged French version) Zbl 1061.65118

Barrault, Maxime; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T.

C. R., Math., Acad. Sci. Paris 339, No. 9, 667-672 (2004).

Summary: We present an efficient reduced-basis discretization procedure for partial differential equations with nonaffine parameter dependence. The method replaces nonaffine coefficient functions with a collateral reduced-basis expansion which then permits an (effectively affine) offline-online computational decomposition. The essential components of the approach are (i) a good collateral reduced-basis approximation space, (ii) a stable and inexpensive interpolation procedure, and (iii) an effective a posteriori estimator to quantify the newly introduced errors. Theoretical and numerical results respectively anticipate and confirm the good behavior of the technique.

MSC:

65N21	Numerical methods for inverse problems for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
35R30	Inverse problems for PDEs

Keywords:

reduced-basis discretization; nonaffine parameter dependence; collateral reduced-basis expansion; interpolation procedure; a posteriori estimator; numerical results; elliptic equation; inverse problem; error bound; finite element method

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