| SC 92-18 | Folkmar A. Bornemann
Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux. Appeared in: Proc. of the Ninth GAMM-Seminar Kiel, 1993 on Adaptive Methods: Algorithms, Theory and Applications. W. Hackbusch, G. Wittum (eds.) Braunschweig: Vieweg 1994, pp. 69-83 |   |
Abstract: A new adaptive approach for
one-dimensional scalar conservation laws with convex flux is
proposed. The initial data are approximated on an adaptive
grid by a problem dependent, monotone interpolation
procedure in such a way, that the multivalued problem of
characteristic transport can be easily and explicitly
solved. The unique entropy solution is chosen by means of a
selection criterion due to LAX. For arbitrary times, the
solutions is represented by an adaptive monotone spline
interpolation. The spatial approximation is controlled by
local 
-error estimated. As a distinctive feature of the
approach, there is no discretization in time. The method is
monotone on fixed grids. Numerical examples are included, to
demonstrate the predicted behavior.
Key words.
method of characteristics, adaptive grids, monotone
interpolation, 
-error estimates
AMS(MOS) subject
classification. 65M15, 65M25, 65M50.
Keywords: method of characteristics,
adaptive grids,
monotone interpolation,
L1-error estimates
MSC: 65M15, 65M25, 65M50