Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux.
Please always quote using this URN: urn:nbn:de:0297-zib-880
- 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.
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| Author: | Folkmar A. Bornemann |
|---|---|
| Document Type: | ZIB-Report |
| Tag: | L1-error estimates; adaptive grids; method of characteristics; monotone interpolation |
| MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M15 Error bounds |
| 65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M25 Method of characteristics | |
| 65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M50 Mesh generation and refinement | |
| Date of first Publication: | 1992/09/01 |
| Series (Serial Number): | ZIB-Report (SC-92-18) |
| ZIB-Reportnumber: | SC-92-18 |
| Published in: | 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 |
