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http://dspace.mediu.edu.my:8181/xmlui/handle/1721.1/3890| Title: | Reduced-Basis Approximation of the Viscosity-Parametrized Incompressible Navier-Stokes Equation: Rigorous A Posteriori Error Bounds |
| Keywords: | reduced-basis a posteriori error estimation output bounds incompressible Navier-Stokes elliptic partial differential equations |
| Issue Date: | 9-Oct-2013 |
| Description: | We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic partial differential equations with affine (or approximately affine) parameter dependence. The essential components are (i) rapidly uniformly convergent global reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) offline/online computational procedures — stratagems which decouple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output of interest and associated error bound — depends only on N (typically very small) and the parametric complexity of the problem.
In this paper we extend our methodology to the viscosity-parametrized incompressible Navier-Stokes equations. There are two critical new ingredients: first, the now-classical Brezzi-Rappaz-Raviart framework for (here, a posteriori) error analysis of approximations of nonlinear elliptic partial differential equations; and second, offline/online computational procedures for efficient calculation of the "constants" required by the Brezzi-Rappaz-Raviart theory — in particular, rigorous lower and upper bounds for the BabuÅ¡ka inf-sup stability and Sobolev "L⁴-H¹" continuity factors, respectively. Numerical results for a simple square-cavity model problem confirm the rapid convergence of the reduced-basis approximation and the good effectivity of the associated a posteriori error bounds. Singapore-MIT Alliance (SMA) |
| URI: | http://koha.mediu.edu.my:8181/xmlui/handle/1721 |
| Other Identifiers: | http://hdl.handle.net/1721.1/3890 |
| Appears in Collections: | MIT Items |
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