Multiresolution schemes for conservation laws

Numerische Mathematik

Volumn 88, Issue 3, 2001, Pages 399-443

  Dahmen, Wolfgang ^a   Gottschlich Müller, Birgit ^a   Müller, Siegfried ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035637177     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s211-001-8009-3     Document Type: Article

References (20)

1. B. Bihari and A. Harten. Multiresolution schemes for the numerical solution of 2-D conservation laws I. SIAM J. Sci. Comput. 18(2), 315-354 (1997)
2. O. Brodersen, M. Hepperle, A. Ronzheimer, C.-C. Rossow, and B. Schöning. Entwicklung des parametrischen Netzgenerierungssystems MegaCads. DLR IB 129-96/1, DLR, 1996
3. J.M. Carnicer, W. Dahmen, and J.M. Peña. Local decomposition of refinable spaces and wavelets. Appl. Comput. Harmon. Anal. 3, 127-153 (1996)
4. A. Cohen, I. Daubechies, and J. Feauveau. Bi-orthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math. 45, 485-560 (1992)
5. W. Dahmen. Stability of multiscale transformations. J. Fourier Anal. Appl. 4, 341-362 (1996)
6. W. Dahmen. Wavelet and multiscale methods for operator equations. Acta Numerica 6, 55-228 (1997)
7. W. Dahmen, A. Kunoth, and K. Urban. Biorthogonal spline-wavelets on the interval - stability and moment conditions. Appl. Comput. Harmon. Anal. 6(2), 132-197 (1999)
8. R.A. DeVore and G.G. Lorentz. Constructive Approximation. Grundlehren der Mathematischen Wissenschaften. Berlin: Springer, 1993
9. B. Gottschlich-Müller. Multiscale Schemes for Multidimensional Conservation Laws. PhD thesis, RWTH Aachen, 1998. Published at Shaker-Verlag, Aachen
10. B. Gottschlich-Müller and S. Müller. On multi-scale concepts for multi-dimensional conservation laws. In W. Hackbusch and G. Wittum, editors, Proceedings of the 13th GAMM-Seminar Kiel on Numerical Treatment of Multi-Scale Problems, January 24th to 26th, 1997, Braunschweig, 1998. Vieweg
11. A. Harten. Multiresolution algorithms for the numerical solution of hyperbolic conservation laws. Comm. Pure Appl. Math. 48(12), 1305-1342 (1995)
12. A. Harten, B. Engquist, S. Osher, and S.R. Chakravarthy. Uniformly high order accurate essentially non-oscillatory schemes III. J. Comp. Phys. 71, 231-303 (1987)
13. D. Kröner. Numerical Schemes for Conservation Laws. Advances in Numerical Mathematics. Wiley-Teubner, 1997
14. R.J. LeVeque. Numerical Methods for Conservation Laws. Birkhäuser, Basel, 2nd edition, 1992
15. S. Müller. Erweiterung von ENO-Verfahren auf zwei Raumdimensionen und Anwendung auf hypersonische Staupunktprobleme. PhD thesis, RWTH Aachen, April 1993
16. P. Roe. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comp. Phys. 43, 357-372 (1981)
17. F. Schröder-Pander and T. Sonar. Preliminary investigations on multiresolution analysis on unstructured grids. DLR Forschungsbericht IB 223-95 A 36, DLR Göttingen, 1995
18. B. Sjögreen. Numerical experiments with the multiresolution scheme for the compressible Euler equations. J. Comp. Phys. 117, 251-261 (1995)
19. W. Sweldens. The lifting scheme: A construction of second generation wavelets. SIAM J. Math. Anal. 29(2), 511-546 (1998)
20. J.F. Thompson, Z.U.A. Warsi, and C.W. Mastin. Numerical Grid Generation: Foundations and Applications. Elsevier: North Holland, 1985