| dc.creator |
Veroy, K. |
|
| dc.creator |
Patera, Anthony T. |
|
| dc.date |
2003-12-14T23:03:25Z |
|
| dc.date |
2003-12-14T23:03:25Z |
|
| dc.date |
2004-01 |
|
| dc.date.accessioned |
2013-10-09T02:32:58Z |
|
| dc.date.available |
2013-10-09T02:32:58Z |
|
| dc.date.issued |
2013-10-09 |
|
| dc.identifier |
http://hdl.handle.net/1721.1/3890 |
|
| dc.identifier.uri |
http://koha.mediu.edu.my:8181/xmlui/handle/1721 |
|
| dc.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. |
|
| dc.description |
Singapore-MIT Alliance (SMA) |
|
| dc.format |
536131 bytes |
|
| dc.format |
application/pdf |
|
| dc.language |
en_US |
|
| dc.relation |
High Performance Computation for Engineered Systems (HPCES); |
|
| dc.subject |
reduced-basis |
|
| dc.subject |
a posteriori error estimation |
|
| dc.subject |
output bounds |
|
| dc.subject |
incompressible Navier-Stokes |
|
| dc.subject |
elliptic partial differential equations |
|
| dc.title |
Reduced-Basis Approximation of the Viscosity-Parametrized Incompressible Navier-Stokes Equation: Rigorous A Posteriori Error Bounds |
|
| dc.type |
Article |
|