TY - GEN A1 - Bornemann, Folkmar A. T1 - Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux. N2 - 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 $L^1$-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. {\bf Key words.} method of characteristics, adaptive grids, monotone interpolation, $L^1$-error estimates {\bf AMS(MOS) subject classification.} 65M15, 65M25, 65M50. T3 - ZIB-Report - SC-92-18 KW - method of characteristics KW - adaptive grids KW - monotone interpolation KW - L1-error estimates Y1 - 1992 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-880 ER -