Free access
Issue
ESAIM: M2AN
Volume 40, Number 3, May-June 2006
Page(s) 469 - 499
DOI http://dx.doi.org/10.1051/m2an:2006020
Published online 22 July 2006
  1. R.L. Actis, B.A. Szabo and C. Schwab, Hierarchic models for laminated plates and shells. Comput. Methods Appl. Mech. Engrg. 172 (1999) 79–107. [CrossRef] [MathSciNet]
  2. V.I. Agoshkov, D. Ambrosi, V. Pennati, A. Quarteroni and F. Saleri, Mathematical and numerical modelling of shallow water flow. Comput. Mech. 11 (1993) 280–299. [CrossRef] [MathSciNet]
  3. V.I. Agoshkov, A. Quarteroni and F. Saleri, Recent developments in the numerical simulation of shallow water equations I: boundary conditions. Appl. Numer. Math. 15 (1994) 175–200. [CrossRef] [MathSciNet]
  4. M. Amara, D. Capatina-Papaghiuc and D. Trujillo, Hydrodynamical modelling and multidimensional approximation of estuarian river flows. Comput. Visual. Sci. 6 (2004) 39–46.
  5. W. Bangerth and R. Rannacher, Adaptive finite element techniques for the acoustic wave equation. J. Comput. Acoust. 9 (2001) 575–591. [CrossRef] [MathSciNet]
  6. Z.P. Bažant, Spurious reflection of elastic waves in nonuniform finite element grids. Comput. Methods Appl. Mech. Engrg. 16 (1978) 91–100. [CrossRef]
  7. R. Becker and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods, in Acta Numerica 2001, A. Iserles Ed., Cambridge University Press, Cambridge, UK (2001).
  8. J.P. Benque, A. Haugel and P.L. Viollet, Numerical methods in environmental fluid mechanics, in Engineering Applications of Computational Hydraulics, M.B. Abbott and J.A. Cunge Eds., Vol. II (1982).
  9. M. Braack and A. Ern, A posteriori control of modeling errors and discretizatin errors. Multiscale Model. Simul. 1 (2003) 221–238. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  10. Ph. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland Publishing Company, Amsterdam (1978).
  11. J.M. Cnossen, H. Bijl, B. Koren and E.H. van Brummelen, Model error estimation in global functionals based on adjoint formulation, in International Conference on Adaptive Modeling and Simulation, ADMOS 2003, N.-E. Wiberg and P. Díez Eds., CIMNE, Barcelona (2003).
  12. A. Ern, S. Perotto and A. Veneziani, Finite element simulation with variable space dimension. The general framework (2006) (in preparation).
  13. M. Feistauer and C. Schwab, Coupling of an interior Navier-Stokes problem with an exterior Oseen problem. J. Math. Fluid. Mech. 3 (2001) 1–17. [CrossRef] [MathSciNet]
  14. L. Formaggia and A. Quarteroni, Mathematical Modelling and Numerical Simulation of the Cardiovascular System, in Handbook of Numerical Analysis, Vol. XII, North-Holland, Amsterdam (2004) 3–127.
  15. L. Formaggia, F. Nobile, A. Quarteroni and A. Veneziani, Multiscale modelling of the circolatory system: a preliminary analysis. Comput. Visual. Sci. 2 (1999) 75–83. [CrossRef]
  16. M.B. Giles and N.A. Pierce, Adjoint equations in CFD: duality, boundary conditions and solution behaviour, in 13th Computational Fluid Dynamics Conference Proceedings (1997) AIAA paper 97–1850.
  17. M.B. Giles and E. Süli, Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality. Acta Numerica 11 (2002) 145–236. [CrossRef] [MathSciNet]
  18. E. Godlewski and P.A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer-Verlag, New York (1996).
  19. A. Griewank and A. Walther, Revolve: an implementation of checkpointing for the reverse or adjoint mode of computational differentiation. ACM T. Math. Software 26 (2000) 19–45. [CrossRef]
  20. I. Harari, Reducing spurious dispersion, anisotropy and reflection in finite element analysis of time-harmonic acoustics. Comput. Methods Appl. Mech. Engrg. 140 (1997) 39–58. [CrossRef] [MathSciNet]
  21. J.L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications. Volume I. Springer-Verlag, Berlin (1972).
  22. G.I. Marchuk, Adjoint Equations and Analysis of Complex Systems. Kluwer Academic Publishers, Dordrecht (1995).
  23. G.I. Marchuk, V.I. Agoshkov and V.P. Shutyaev, Adjoint equations and perturbation algorithms in nonlinear problems. CRC Press (1996).
  24. S. Micheletti and S. Perotto (2006) (in preparation).
  25. E. Miglio, S. Perotto and F. Saleri, A multiphysics strategy for free-surface flows, Domain Decomposition Methods in Science and Engineering, R. Kornhuber, R.H.W. Hoppe, J. Périaux, O. Pironneau, O. Widlund, J. Xu Eds., Springer-Verlag, Lect. Notes Comput. Sci. Engrg. 40 (2004) 395–402.
  26. E. Miglio, S. Perotto and F. Saleri, Model coupling techniques for free-surface flow problems. Part I. Nonlinear Analysis 63 (2005) 1885–1896. [CrossRef]
  27. J.T. Oden and S. Prudhomme, Estimation of modeling error in computational mechanics. J. Comput. Phys. 182 (2002) 469–515.
  28. J.T. Oden and K.S. Vemaganti, Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. I. Error estimates and adaptive algorithms. J. Comput. Phys. 164 (2000) 22–47. [CrossRef] [MathSciNet]
  29. J.T. Oden and K.S. Vemaganti, Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. II. A computational environment for adaptive modeling of heterogeneous elastic solids. Comput. Methods Appl. Mech. Engrg. 190 (2001) 6089–6124. [CrossRef] [MathSciNet]
  30. J.T. Oden, S. Prudhomme, D.C. Hammerand and M.S. Kuczma, Modeling error and adaptivity in nonlinear continuum mechanics. Comput. Method. Appl. M. 190 (2001) 6663–6684. [CrossRef]
  31. A. Quarteroni and L. Stolcis, Heterogeneous domain decomposition for compressible flows, in Proceedings of the ICFD Conference on Numerical Methods for Fluid Dynamics, M. Baines and W.K. Morton Eds., Oxford University Press, Oxford (1995) 113–128.
  32. A. Quarteroni and A. Valli, Domain decomposition methods for partial differential equations. Oxford University Press Inc., New York (1999).
  33. M. Schulz and G. Steinebach, Two-dimensional modelling of the river Rhine. J. Comput. Appl. Math. 145 (2002) 11–20. [CrossRef] [MathSciNet]
  34. E. Stein and S. Ohnimus, Anisotropic discretization- and model-error estimation in solid mechanics by local Neumann problems. Comput. Methods Appl. Mech. Engrg. 176 (1999) 363–385. [CrossRef] [MathSciNet]
  35. G.S. Stelling, On the construction of computational models for shallow water equations. Rijkswaterstaat Communication 35 (1984).
  36. C.B. Vreugdenhil, Numerical Methods for Shallow-Water Flows. Kluwer Academic Press, Dordrecht (1998).
  37. G.B. Whitham, Linear and Nonlinear Waves. Wiley, New York (1974).
  38. F.W. Wubs, Numerical solution of the shallow-water equations. CWI Tract, 49, F.W. Wubs Ed., Amsterdam (1988).

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