Numerical Analysis Seminar

Wednesday, October 31, 2007

Speaker: Bojan Popov Department of Mathematics, Texas A&M University
Title: Second order schemes and entropy
Time: 3:00-4:00 pm
Place: Blocker 628

Abstract

We will consider a class of Godunov-type second order schemes for nonlinear conservation laws. In the usual design of such schemes one uses the so-called limiters to prevent them from oscillating. In this talk we will show that one such scheme, the Nessyahu-Tadmor scheme, is weakly consistent with a single cell entropy inequality. That in turn implies that the Nessyahu-Tadmor Scheme converges strongly in L1 to the entropy solution of the problem for a scalar strictly convex conservation law with bounded initial data. This result seems to be new and somewhat surprising because second order schemes are designed to be non-oscillatory or TVD and the usual convergence results require initial data of bounded variation. Some possible extensions to one dimensional systems will be discussed.

Last revised: 09/30/07 By: abnersg@math