Free Access
Volume 44, Number 2, March-April 2010
Page(s) 289 - 322
Published online 27 January 2010
  1. E.J. Allen, S.J. Novosel and Z. Zhang, Finite element and difference approximation of some linear stochastic partial differential equations. Stoch. Stoch. Rep. 64 (1998) 117–142.
  2. I. Babuška, R. Tempone and G.E. Zouraris, Galerkin finite element approximations of stochastic elliptic partial differential equations. SIAM J. Numer. Anal. 42 (2004) 800–825. [CrossRef] [MathSciNet]
  3. L. Bin, Numerical method for a parabolic stochastic partial differential equation. Master Thesis 2004-03, Chalmers University of Technology, Göteborg, Sweden (2004).
  4. J.H. Bramble and S.R. Hilbert, Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation. SIAM J. Numer. Anal. 7 (1970) 112–124. [CrossRef] [MathSciNet]
  5. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York, USA (1994).
  6. C. Cardon-Weber, Implicit approximation scheme for the Cahn-Hilliard stochastic equation. PMA 613, Laboratoire de Probabilités et Modèles Alétoires, CNRS U.M.R. 7599, Universtités Paris VI et VII, Paris, France (2000).
  7. C. Cardon-Weber, Cahn-Hilliard equation: existence of the solution and of its density. Bernoulli 7 (2001) 777–816. [CrossRef] [MathSciNet]
  8. P.G. Ciarlet, The finite element methods for elliptic problems. North-Holland, New York (1987).
  9. H. Cook, Browian motion in spinodal decomposition. Acta Metall. 18 (1970) 297–306. [CrossRef]
  10. G. Da Prato and A. Debussche, Stochastic Cahn-Hilliard equation. Nonlinear Anal. 26 (1996) 241–263. [CrossRef] [MathSciNet]
  11. N. Dunford and J.T. Schwartz, Linear Operators. Part II. Spectral Theory. Self Adjoint Operators in Hilbert Space. Reprint of the 1963 original, Wiley Classics Library, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, USA (1988).
  12. K.R. Elder, T.M. Rogers and R.C. Desai, Numerical study of the late stages of spinodal decomposition. Phys. Rev. B 37 (1987) 9638–9649.
  13. G.H. Golub and C.F. Van Loan, Matrix Computations. Second Edition, The John Hopkins University Press, Baltimore, USA (1989).
  14. W. Grecksch and P.E. Kloeden, Time-discretised Galerkin approximations of parabolic stochastic PDEs. Bull. Austral. Math. Soc. 54 (1996) 79–85. [CrossRef] [MathSciNet]
  15. E. Hausenblas, Numerical analysis of semilinear stochastic evolution equations in Banach spaces. J. Comput. Appl. Math. 147 (2002) 485–516. [CrossRef] [MathSciNet]
  16. E. Hausenblas, Approximation for semilinear stochastic evolution equations. Potential Anal. 18 (2003) 141–186. [CrossRef] [MathSciNet]
  17. G. Kallianpur and J. Xiong, Stochastic Differential Equations in Infinite Dimensional Spaces, Lecture Notes-Monograph Series 26. Institute of Mathematical Statistics, Hayward, USA (1995).
  18. L. Kielhorn and M. Muthukumar, Spinodal decomposition of symmetric diblock copolymer homopolymer blends at the Lifshitz point. J. Chem. Phys. 110 (1999) 4079–4089. [CrossRef]
  19. P.E. Kloeden and S. Shot, Linear-implicit strong schemes for Itô-Galerkin approximations of stochastic PDEs. J. Appl. Math. Stoch. Anal. 14 (2001) 47–53. [CrossRef]
  20. G.T. Kossioris and G.E. Zouraris, Fully-Discrete Finite Element Approximations for a Fourth-Order Linear Stochastic Parabolic Equation with Additive Space-Time White Noise. TRITA-NA 2008:2, School of Computer Science and Communication, KTH, Stockholm, Sweden (2008).
  21. J.L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol. I. Springer-Verlag, Berlin-Heidelberg, Germany (1972).
  22. T. Müller-Gronbach and K. Ritter, Lower bounds and non-uniform time discretization for approximation of stochastic heat equations. Found. Comput. Math. 7 (2007) 135–181. [CrossRef] [MathSciNet]
  23. J. Printems, On the discretization in time of parabolic stochastic partial differential equations. ESAIM: M2AN 35 (2001) 1055–1078. [CrossRef] [EDP Sciences]
  24. V. Thomée, Galerkin Finite Element Methods for Parabolic Problems, Spriger Series in Computational Mathematics 25. Springer-Verlag, Berlin-Heidelberg, Germany (1997).
  25. Y. Yan, Error analysis and smothing properies of discretized deterministic and stochastic parabolic problems. Ph.D. Thesis, Department of Computational Mathematics, Chalmers University of Technology and Göteborg University, Göteborg, Sweden (2003).
  26. Y. Yan, Semidiscrete Galerkin approximation for a linear stochastic parabolic partial differential equation driven by an additive noise. BIT 44 (2004) 829–847. [CrossRef] [MathSciNet]
  27. Y. Yan, Galerkin finite element methods for stochastic parabolic partial differential equations. SIAM J. Numer. Anal. 43 (2005) 1363–1384. [CrossRef] [MathSciNet]
  28. J.B. Walsh, An introduction to stochastic partial differential equations., Lecture Notes in Mathematics 1180. Springer Verlag, Berlin-Heidelberg, Germany (1986) 265–439.
  29. J.B. Walsh, Finite element methods for parabolic stochastic PDEs. Potential Anal. 23 (2005) 1–43. [CrossRef] [MathSciNet]

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