Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values

TL;DR

This paper introduces a reduced basis method with rigorous error bounds for efficiently solving parametrized viscous Burgers equations, significantly reducing computational costs while maintaining accuracy.

Contribution

It develops an offline/online reduced basis approach with certified error bounds for the viscous Burgers equation with variable parameters.

Findings

Significant computational savings demonstrated.

Efficient and rigorous error bounds validated.

Applicable to parametrized initial and boundary data.

Abstract

We present a reduced basis offline/online procedure for viscous Burgers initial boundary value problem, enabling efficient approximate computation of the solutions of this equation for parametrized viscosity and initial and boundary value data. This procedure comes with a fast-evaluated rigorous error bound certifying the approximation procedure. Our numerical experiments show significant computational savings, as well as efficiency of the error bound.