Adaptivity in space and time for shallow water equations

International Journal for Numerical Methods in Fluids

Volumn 31, Issue 1, 1999, Pages 285-297

  Morandi Cecchi, M ^a   Marcuzzi, F ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

a posteriori error estimates; Mesh adaptation; Shallow waters; Time step control

Indexed keywords

ERROR; MATHEMATICAL MODELING; SHALLOW-WATER EQUATION;

EID: 0344500603     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0363(19990915)31:1<285::AID-FLD969>3.0.CO;2-6     Document Type: Article

References (12)

1. M. Morandi Cecchi, A. Pica and E. Secco, 'A projection method for shallow water equations', Int. J. Numer. Methods Fluids, 27, 81-95 (1998).
2. M. Morandi Cecchi and L. Salasnich, 'Shallow water theory and its application to the Venice Lagoon', Comput. Methods Appl. Mech. Eng., 151, 63-74 (1998).
3. O.G. Zienkiewicz, J. Wu and J. Peraire, 'A new semi-implicit or explicit algorithm for shallow water equations', Math. Model. Sci. Comput., 1, 31-49 (1993).
4. R. Verfurth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley-Teubner, 1997.
5. K. Eriksson, D. Estep, P. Hansbo and C. Johnson, 'Introduction to adaptive methods for differential equations', Acta Numer., 105-179 (1995).
6. J. Donea, 'A Taylor-Galerkin method for convective transport problems', Int. J. Numer. Methods Eng., 20, 101-119 (1984).
7. O.C. Zienkiewicz and J.Z. Zhu, 'A simple error estimator and adaptive procedure for practical engineering analysis', Int. J. Numer. Methods Eng., 24, 337-357 (1987).
8. T.J.R. Hughes, The Finite Element Method, Prentice-Hall, Englewood Cliff, NJ, 1987.
9. M. Morandi Cecchi and L. Salasnich, 'Convergence of the splitting method for shallow water equations', AIICSR 97, Smolenice, Slovakia, 1997, pp. 1-12.
10. V. Thomee, 'Finite difference methods for linear parabolic equations', in P.G. Ciarlet and J.L. Lions (eds.), Handbook of Numerical Analysis, North-Holland, Amsterdam, 1991, pp. 12-171.
11. R. Rodriguez, 'Some remarks on Zienkiewicz-Zhu estimator', Numer. Methods PDE, 10, 625-635 (1994).
12. E. Hairer, S.P.N. Torsett and G. Wanner, Solving Ordinary Differential Equations I, Springer-Verlag, Berlin, 1987.