Collaborator: R. DeVore
Sponsor: ONR
The primary focus of research sponsored by this grant has been the regularity of solutions to scalar conservation laws and numerical recovery of "shocks" in several space dimensions. DeVore and Lucier have initiated investigations into multidimensional scalar conservation laws with the hope of extending their univariate results to this setting. Their previous results show:
(i) the Besov spaces 
, 
, 
(roughly speaking, these are the spaces of functions with 
derivatives in 
) are regularity spaces for scalar conservation laws in one space dimension, and (ii) there are numerical methods based on moving grids that can achieve arbitrary prescribed orders of approximation, namely, for any initial condition in 
, the solution can be recovered to error 
in the metric of 
by a numerical method based on moving grids.