Solution of time-dependent advection-diffusion problems with the sparse-grid combination technique and a rosenbrock solver

Computational Methods in Applied Mathematics

Volumn 1, Issue 1, 2001, Pages 86-98

  Lastdrager, Boris ^a   Koren, Barry ^a   Verwer, Jan ^a  

^a CWI   (Netherlands)

Author keywords

Advection Diffusion problems; Combination techniques; Error analysis; Rosenbrock methods; Sparse grids

Indexed keywords

EID: 0042139034     PISSN: 16094840     EISSN: 16099389     Source Type: Journal    
DOI: 10.2478/cmam-2001-0006     Document Type: Article

References (14)

1. H. J. Bungartz, M. Griebel, D. Roschke, and C. Zenger, Pointwise convergence of the combination technique for the laplace equation, East-West J. Numer. Math., 2 (1994), No. 1, pp. 21-45.
2. K. Dekker and J. G. Verwer, Stability of Runga-Kutta Methods for Stiff Nonlinear Differential Equations, Elsevier North-Holland, Amsterdam, 1984.
3. M. Griebel, The combination technique for the sparse grid solution ofpde's on multiprocessor machines, Parallel Processing Letters, 2 (1992), No. 1, pp. 61-70.
4. M. Griebel, M. Schneider, and C. Zenger, A combination technique for the solution of sparse grid problems, in: Iterative Methods in Linear Algebra (R. Beauwens and P. de Groen, eds.), North-Holland, Amsterdam, 1992, pp. 263-281.
5. M. Griebel and G. Zumbusch, Adaptive sparse grids for hyperbolic conservation laws, in: Notes on Numerical Fluid Mechanics (W. Hackbusch and G. Wittum, eds.), Vieweg, Braunschweig, 1999
6. B. Koren, A robust upwind discretization method for advection, diffusion and source terms, in: Numerical Methods for Advection-Diffusion Problems (C. B. Vreugdenhil and B. Koren, eds.), vol. 45 of Notes on Numerical Fluid Mechanics, Vieweg, Braunschweig, 1993, pp. 117-138.
7. D. Lanser, J. G. Blom, and J. G. Verwer, Time integration of the shallow water equations in spherical geometry, Report mas-r0021, CWI, Amsterdam, 2000, http://www.cwi.nl/static/publications/reports/MAS-2000.html.
8. B. Lastdrager and B. Koren, Error analysis for function representation by the sparse-grid combination technique, Report mas-r9823, CWI, Amsterdam, 1998, http://www.cwi.nl/static/publications/reports/MAS-1999.html.
9. B. Lastdrager, B. Koren, and J. G. Verwer, The sparse-grid combination technique applied to time-dependent advection problems, Report mas-r9930, CWI, Amsterdam, 1999, http://www.cwi.nl/static/publications/reports/MAS-1999.html.
10. B. Lastdrager, B. Koren, and J. G. Verwer, The sparse-grid combination technique applied to time-dependent advection problems, in: Proceedings of the Sixth European Multigrid Conference, Gent, 1999 (E. Dick, K. Riemslagh, and J. Vierendeels, eds.), vol. 14 of Lecture Notes in Computational Science and Engineering, Springer, Berlin, 2000, pp. 143-149.
11. U. Rüde, Multilevel, extrapolation and sparse grid methods, in: Multigrid Methods (P. W. Hemker and P. Wesseling, eds.), vol. IV, Birkhauser, Basel, 1993, pp. 281-294.
12. L. F. Shampine, Numerical Solution of Ordinary Differential Equations, Chapman & Hall, New York, 1994.
13. J. G. Verwer, E. J. Spee, J. G. Blom, and W. Hundsdorfer, A second-order rosenbrock method applied to photochemical dispersion problems, SIAM J. Sci. Comput., 20 (1999), No. 4, pp. 1456-1480.
14. C. Zenger, Sparse grids, vol. 31 of Notes on Numerical Fluid Mechanics, Vieweg, Braunschweig, 1991, pp. 241-251.