CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

                  UNIVERSITY OF COLORADO AT DENVER



TITLE:   A posteriori error estimates for nonlinear conservation laws
 

SPEAKER: Bernardo Cockburn, School of Mathematics, University of Minnesota
         

DATE:    Monday, February 3, 1997


PLACE:   Seminar Room 641 
         UCD Building, 1250 14th St., Denver


TIME:    noon (Refreshments served at 11:45 am)



ABSTRACT

          A posteriori error estimates for nonlinear scalar
          conservation laws have been available in the literature
          since the 1976 work of Kuznetsov. However, they were used
          to estimate rates of convergence rather than to device
          adaptivity strategies for obtaining numerical approximations.
          In this talk, we concern ourselves with the simplest version
          of the a posteriori error estimates available and explore
          how good the estimator is. We show, numerically, that if the
          solution is smooth, the estimator is at most 1.3 times the
          actual error. We also show that if the solution is discontinuous
          and the convective term linear, this is also the case. We prove
          that in the nonlinear case, however, the estimator cannot be
          sharp. We identify the mechanism that causes this undesirable 
          effect.