Free access
Issue
ESAIM: M2AN
Volume 42, Number 5, September-October 2008
Page(s) 777 - 819
DOI http://dx.doi.org/10.1051/m2an:2008027
Published online 30 July 2008
  1. K. Babenko, Approximation by trigonometric polynomials is a certain class of periodic functions of several variables. Soviet Math. Dokl. 1 (1960) 672–675. Russian original in Dokl. Akad. Nauk SSSR 132 (1960) 982–985. [MathSciNet]
  2. J.W. Barrett and E. Süli, Existence of global weak solutions to kinetic models of dilute polymers. Multiscale Model. Simul. 6 (2007) 506–546. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  3. J.W. Barrett, C. Schwab and E. Süli, Existence of global weak solutions for some polymeric flow models. Math. Models Methods Appl. Sci. 15 (2005) 939–983. [CrossRef] [MathSciNet]
  4. R.F. Bass, Diffusion and Elliptic Operators. Springer-Verlag, New York (1997).
  5. T.S. Blyth and E.F. Robertson, Further Linear Algebra. Springer-Verlag, London (2002).
  6. H.-J. Bungartz, Finite elements of higher order on sparse grids. Habilitation thesis, Informatik, TU München, Aachen: Shaker Verlag (1998).
  7. H.-J. Bungartz and M. Griebel, Sparse grids. Acta Numer. 13 (2004) 1–123. [CrossRef] [MathSciNet]
  8. R. DeVore, S. Konyagin and V. Temlyakov, Hyperbolic wavelet approximation. Constr. Approx. 14 (1998) 1–26. [CrossRef] [MathSciNet]
  9. J. Dick, I.H. Sloan, X. Wang and H. Woźniakowski, Good lattice rules in weighted Korobov spaces with general weights. Numer. Math. 103 (2006) 63–97. [CrossRef] [MathSciNet]
  10. J. Elf, P. Lötstedt and P. Sjöberg, Problems of high dimension in molecular biology, in Proceedings of the 19th GAMM-Seminar Leipzig, W. Hackbusch Ed. (2003) 21–30.
  11. M. Griebel, Sparse grids and related approximation schemes for higher dimensional problems, in Foundations of Computational Mathematics 2005, L.-M. Pardo, A. Pinkus, E. Süli, M. Todd Eds., Cambridge University Press (2006) 106–161.
  12. V.H. Hoang and C. Schwab, High dimensional finite elements for elliptic problems with multiple scales. Multiscale Model. Simul. 3 (2005) 168–194. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  13. L. Hörmander, The Analysis of Linear Partial Differential Operators II: Differential Operators with Constant Coefficients. Springer-Verlag, Berlin, Reprint of the 1983 edition (2005).
  14. P. Houston and E. Süli, Stabilized hp-finite element approximation of partial differential equations with non-negative characteristic form. Computing 66 (2001) 99–119. [CrossRef] [MathSciNet]
  15. P. Houston, C. Schwab and E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002) 2133–2163. [CrossRef] [MathSciNet]
  16. B. Lapeyre, É. Pardoux and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford Texts in Applied and Engineering Mathematics. Oxford University Press, Oxford (2003).
  17. P. Laurençot and S. Mischler, The continuous coagulation fragmentation equations with diffusion. Arch. Rational Mech. Anal. 162 (2002) 45–99. [CrossRef]
  18. C. Le Bris and P.-L. Lions, Renormalized solutions of some transport equations with W1,1 velocities and applications. Annali di Matematica 183 (2004) 97–130. [CrossRef] [MathSciNet]
  19. E. Novak and K. Ritter, The curse of dimension and a universal method for numerical integration, in Multivariate Approximation and Splines, G. Nürnberger, J. Schmidt and G. Walz Eds., International Series in Numerical Mathematics, Birkhäuser, Basel (1998) 177–188.
  20. O.A. Oleĭnik and E.V. Radkevič, Second Order Equations with Nonnegative Characteristic Form. American Mathematical Society, Providence, RI (1973).
  21. H.-C. Öttinger, Stochastic Processes in Polymeric Fluids. Springer-Verlag, New York (1996).
  22. H.-G. Roos, M. Stynes and L. Tobiska, Numerical Methods for Singularly Perturbed Differential Equations. Convection-Diffusion and Flow Problems, Springer Series in Computational Mathematics 24. Springer-Verlag, New York (1996).
  23. C. Schwab, p- and hp-Finite Element Methods: Theory and Applications in Solid and Fluid Mechanics, Numerical Methods and Scientific Computation. Clarendon Press, Oxford (1998).
  24. S. Smolyak, Quadrature and interpolation formulas for products of certain classes of functions. Soviet Math. Dokl. 4 (1963) 240–243. Russian original in Dokl. Akad. Nauk SSSR 148 (1963) 1042–1045.
  25. E. Süli, Finite element approximation of high-dimensional transport-dominated diffusion problems, in Foundations of Computational Mathematics 2005, L.-M. Pardo, A. Pinkus, E. Süli, M. Todd Eds., Cambridge University Press (2006) 343–370. Available at: http://web.comlab.ox.ac.uk/oucl/publications/natr/index.html
  26. E. Süli, Finite element algorithms for transport-diffusion problems: stability, adaptivity, tractability, in Invited Lecture at the International Congress of Mathematicians, Madrid, 22–30 August 2006. Available at: http://web.comlab.ox.ac.uk/work/endre.suli/Suli-ICM2006.pdf
  27. V. Temlyakov, Approximation of functions with bounded mixed derivative, in Proc. Steklov Inst. of Math. 178, American Mathematical Society, Providence, RI (1989).
  28. N.G. van Kampen, Stochastic Processes in Physics and Chemistry. Elsevier, Amsterdam (1992).
  29. T. von Petersdorff and C. Schwab, Numerical solution of parabolic equations in high dimensions. ESAIM: M2AN 38 (2004) 93–128. [CrossRef] [EDP Sciences]
  30. G. Wasilkowski and H. Woźniakowski, Explicit cost bounds of algorithms for multivariate tensor product problems. J. Complexity 11 (1995) 1–56. [CrossRef] [MathSciNet]
  31. C. Zenger, Sparse grids, in Parallel Algorithms for Partial Differential Equations, W. Hackbusch Ed., Notes on Numerical Fluid Mechanics 31, Vieweg, Braunschweig/Wiesbaden (1991).
  32. G.W. Zumbusch, A sparse grid PDE solver, in Advances in Software Tools for Scientific Computing, H.P. Langtangen, A.M. Bruaset and E. Quak Eds., Lecture Notes in Computational Science and Engineering 10, Springer, Berlin (Proceedings SciTools '98) (2000) 133–177.

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