Gauss - Newton Multilevel Methods for Least-Squares Finite Element Computations of Variably Saturated Subsurface Flow

Computing (Vienna/New York)

Volumn 64, Issue 4, 2000, Pages 323-338

  Starke, Gerhard ^a  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

Inexact Gauss Newton method; Least squares finite element method; Multilevel method; Nonlinear elliptic problems; Raviart Thomas spaces; Variably saturated flow

Indexed keywords

EID: 0042229477     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s006070070028     Document Type: Article

References (15)

1. Arnold, D. N., Falk, R. S., Winther, R.: Preconditioning in H(div) with applications. Math. Comp. 66, 957-984 (1997).
2. Berndt, M., Manteuffel, T. A., McCormick, S. F.: Local error estimates and adaptive refinement for first-order system least squares. Electr. Trans. Numer. Anal. 6, 35-43 (1997).
3. Brezzi, F., Fortin, M.: Mixed and hybrid finite element methods. New York: Springer 1991.
4. Cai, Z., Lazarov, R., Manteuffel, T. A., McCormick S. F.: First-order system least squares for second-order partial differential equations: Part I. SIAM J. Numer. Anal. 31, 1785-1799 (1994).
5. Carsel R. F., Parrish, R. S.: Developing joint probability distributions of soil water retention characteristics. Water Resources Res. 24, 755-769 (1988).
6. Dennis, J. E., Schnabel, R. B.: Numerical methods for unconstrained optimization and nonlinear equations. Philadelphia: SIAM 1996.
7. Fuhrmann, J.: Zur Verwendung von Mehrgitterverfahren bei der numerischen Behandlung elliptischer partieller Differentialgleichungen mit variablen Koeffizienten, PhD thesis, Technische Universität Chemnitz-Zwickau, Aachen 1995.
8. Helmig, R.: Multiphase flow and transport processes in the subsurface. Berlin Heidelberg New York Tokyo: Springer 1997.
9. Korsawe, J., Starke, G.: Multilevel projection methods for nonlinear least-squares finite element computations. Electr. Trans. Numer. Anal. (1999) (to appear).
10. Mualem, Y.: A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Res. 12, 513-522 (1976).
11. Raviart, P. A., Thomas, J. M.: A mixed finite element method for second order elliptic problems. In: Mathematical aspects of the finite element method (Galligani, E. M. I., ed.), pp. 292-315. Berlin Heidelberg New York: Springer, 1977.
12. Starke, G.: Adaptive least-squares Galerkin methods for parabolic problems. SIAM J. Numer. Anal, (in preparation).
13. Starke, G.: Least-squares mixed finite element solution of variably saturated subsurface flow problems. SIAM J. Sci. Comput. 20 (to appear).
14. Van Genuchten, M. T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892-898 (1980).
15. Vauclin, M., Khanji, D., Vachaud, G.: Experimental and numerical study of a transient, two-dimensional unsaturated-saturated water table recharge problem. Water Resources Res. 15, 1089-1101 (1979).