An adaptive finite element method for modeling salt diapirism

Mathematical Models and Methods in Applied Sciences

Volumn 16, Issue 4, 2006, Pages 587-614

  Massimi, P ^a   Quarteroni, A ^a,b   Scrofani, G ^a  

^a POLITECNICO DI MILANO   (Italy)

^b EPFL   (Switzerland)

Author keywords

Finite element methods; Interface tracking; Salt diapirism; Subsurface geology; Tectonics

Indexed keywords

EID: 33645963166     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202506001273     Document Type: Article

References (27)

1. S. Zaleski and P. Julien, Numerical simulation of salt diapir formation in small and extended geometries, Tectonophys. 206 (1992) 55-69.
2. C. J. Talbot, Halokinesis and thermal convection, Nature 273 (1978) 739- 741.
3. D. D. Schultz-Ela, M. P. A. Jackson and B. C. Vendeville, Mechanics of active salt diapirism, Tectonophys. 228 (1993) 275-312.
4. A. T. Ismail-Zadeh, A. I. Korotkii, B. M. Naimark, A. P. Suetov and I. A. Tsepelev, Implementation of a three-dimensional hydrodynamic model for evolution of sedimentary basins, Comput. Math. Math. Phys. 38 (1998) 1138-1151.
5. A. T. Ismail-Zadeh, C. J. Talbot and Yu. A. Volozh, Dynamic restoration of profiles across diapiric salt structures: numerical approach and its application, Tectonophys. 337 (2001) 21-36.
6. A. Poliakov, R. van Balen, Y. Podladchikov, B. Daudre, S. Cloetingh and C. Talbot, Numerical analysis of how sedimentation and redistribution of surficial sediments affects salt diapirism, Tectonophys. 226 (1993) 199-216.
7. A. Poliakov and Y. Podladchikov, Diapirism and topography, Geophys. J. Int. 109 (1992) 553-564.
8. A. Poliakov, Y. Podladchikov and C. Talbot, Numerical model of complex diapirism, Tectonophys. 228 (1993) 189-198.
9. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Instability (Oxford Univ. Press, 1961).
10. A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations (Springer-Verlag, 1997).
11. P. L. Lions, Mathematical Topics in Fluid Mechanics, Vol. 1: Incompressible Models (Oxford Univ. Press, 1996).
12. S. Antontsev, A. Meirmanov and B. V. Yurinsky, A free-boundary problem for Stokes equations: Classical solutions, Interfaces Free Bound. 2 (2000) 413-424.
13. F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multiplier, R.A.I.R.O. Anal. Nuḿer. 8 (1974) 129-151.
14. E. Creuse, S. Nicaise and G. Kunert, A posteriori error estimation for the Stokes problem: Anisotropic and isotropic discretizations, Math. Mod. Meth. Appl. Sci. 14 (2004) 1927-1341.
15. C. Bernardi, V. Girault and F. Hecht, A posteriori analysis of a penalty methods and application to the Stokes problem, Math. Mod. Meth. Appl. Sci. 13 (2003) 1599-1628.
16. P. L. George and H. Borouchaki, Delaunay Triangulation and Meshing- Application to Finite Element (Editions Hermes, 1998).
17. L. F. Athy, Density, porosity, and compaction of sedimentary rock, Amer. Ass. Petrol. Geol. Bull. 14 (1930) 1-22.
18. C. M. Bethke, A numerical model of compaction-driven grownd water flow and heat transfer and its application to the paleohydrology of intractatonic sedimentary basins, J. Geophys. Res. 90 (1985) 6817-6828.
19. D. M. Audet and A. C. Fowler, A mathematical model for compaction in sedimentary basins, Geophys. J. Int. 110 (1992) 577-590.
20. S. X. Yang, Mathematical Modelling of Compaction and Diagenesis in Sedimentary Basins, Ph.D. Thesis, Oxford, 1997.
21. A. C. Fawler and S. X. Yang, Fast and slow compaction in sedimentary basins, SIAM J. Appl. Math. 59 (1998) 365-385.
22. T. A. Davis and I. S. Duff, Unsymmetric-pattern multifrontal method for sparse LU factorization, SIAM J. Matrix Anal. Appl. 18 (1997) 140-158.
23. D. Peric and A. J. L. Crook, Computatoinal strategies for predictive geology with reference to salt tectonics, Comput. Meth. Appl. Mech. Engrg. 193 (2004) 5195-5222.
24. M. Discacciati and A. Quarteroni, Analysis of a domain decomposition method for the coupling Stokes and Darcy equations. In Numerical Mathematics and Advanced Applications, eds. F. Brezzi, A. Buffa, S. Corsaro and A. Murli (Springer, 2003).
25. M. Discacciati and A. Quarteroni, Convergence analysis of a subdomain iterative method for finite element approximation of the coupling Stokes and Darcy equations, Comput. Visual Sci. 6 (2004) 93-103.
26. M. Discacciati, Domain Decomposition Methods for the Coupling Surface and Grvund- water Flows, Ph.D. Thesis, Lausanne, 2004.
27. H. Ge, M. P. A. Jackson and B. C. Vendeville, Kinematics and dynamics of salt tectonics driven by progradation, AAPG Bull. 81 (1997) 398-423.