Reduced Basis Approximation and A Posteriori Error Estimation for the Time- Dependent Viscous Burgers Equation

• Published in: Calcolo, vol. 46, num. 3, p. 157--185
• Publication date: 2009

In this paper we present rigorous a posteriori L2 error bounds for reduced basis approximations of the unsteady viscous Burgers equation in one space dimension. The key new ingredient is accurate solution-dependent (Online) calculation of the exponential-in-time stability factor by the Successive Constraint Method. Numerical results indicate that the a posteriori error bounds are practicable for reasonably large times — many convective scales — and reasonably large Reynolds numbers — O(100) or larger. Work in progress (in collaboration with Dr Paul Fischer) considered the full unsteady incompressible Navier-Stokes equation.

Note: previously EPFL-IACS Report 10.2008

Keywords: time-dependent viscous Burgers equation ; reduced basis approximation ; a posteriori error estimation ; error bounds ; exponential-in-time stability factor

Reference

• CMCS-ARTICLE-2008-025
• doi:10.1007/s10092-009-0005-x
• View record in Web of Science

• URL: http://augustine.mit.edu/methodology/papers/atpCalcoloJun2008preprint.pdf

Record created on 2008-06-18, modified on 2012-03-21