Free Access
Issue |
ESAIM: M2AN
Volume 50, Number 6, November-December 2016
|
|
---|---|---|
Page(s) | 1699 - 1730 | |
DOI | https://doi.org/10.1051/m2an/2016004 | |
Published online | 18 October 2016 |
- Y. Achdou and M. Falcone, A semi-Lagrangian scheme for mean curvature motion with nonlinear Neumann conditions. Interfaces Free Bound. 14 (2012) 455–485. [CrossRef] [MathSciNet] [Google Scholar]
- O. Bokanowski and F. Bonnans, Semi-lagrangian schemes for second order equations. In preparation (2016). [Google Scholar]
- O. Bokanowski, Y. Cheng and C.-W. Shu, Convergence of some Discontinuous Galerkin schemes for nonlinear Hamilton-Jacobi equations. Math. Comp. 85 (2016) 2131–2159. [CrossRef] [MathSciNet] [Google Scholar]
- F. Camilli and M. Falcone, An approximation scheme for the optimal control of diffusion processes. RAIRO Modél. Math. Anal. Numér. 29 (1995) 97–122. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- E. Carlini, R. Ferretti and G. Russo, A weighted essentialy non oscillatory, large time-step scheme for Hamilton Jacobi equations. SIAM J. Sci. Comp. 27 (2005) 1071–1091. [CrossRef] [Google Scholar]
- P.G. Ciarlet, Finite Element Method for Elliptic Problems. NorthHolland, Amsterdam (1978). [Google Scholar]
- B. Cockburn, Discontinuous Galerkin methods. ZAMM Z. Angew. Math. Mech. 83 (2003) 731–754. [CrossRef] [MathSciNet] [Google Scholar]
- B. Cockburn and C.-W. Shu, Runge-kutta discontinuous galerkin methods for convection-dominated problems. J. Comput. Phys. 223 (2007) 398–415. [CrossRef] [MathSciNet] [Google Scholar]
- N. Crouseilles, M. Mehrenberger and F. Vecil, Discontinuous Galerkin semi-Lagrangian method for Vlasov–Poisson. In CEMRACS’10 research achievements: numerical modeling of fusion. ESAIM Proc. 32 (2011) 211–230. [CrossRef] [EDP Sciences] [Google Scholar]
- K. Debrabant, Runge-Kutta methods for third order weak approximation of SDEs with multidimensional additive noise. BIT 50 (2010) 541–558. [CrossRef] [MathSciNet] [Google Scholar]
- K. Debrabant and E.R. Jakobsen, Semi-Lagrangian schemes for linear and fully non-linear diffusion equations. Math. Comp. 82 (2013) 1433–1462. [CrossRef] [MathSciNet] [Google Scholar]
- F. Faà di Bruno, Note sur une nouvelle formule de calcul différentiel. Quarterly J. Pure Appl. Math. 1 (1857) 359–360. See also http://en.wikipedia.org/wiki/Faa˙di˙Bruno’s˙formula. [Google Scholar]
- M. Falcone and R. Ferretti, Convergence analysis for a class of high-order semi-Lagrangian advection schemes. SIAM J. Numer. Anal. 35 (1998) 909–940. [CrossRef] [MathSciNet] [Google Scholar]
- M. Falcone and R. Ferretti, Semi-Lagrangian approximation schemes for linear and Hamilton-Jacobi equations. Society for Industrial and Applied Mathematics SIAM, Philadelphia, PA (2014). [Google Scholar]
- R. Ferretti, Convergence of semi-Lagrangian approximations to convex Hamilton-Jacobi equations under (very) large Courant numbers. SIAM J. Numer. Anal. 40 (2002) 2240–2253. [CrossRef] [MathSciNet] [Google Scholar]
- R. Ferretti, A technique for high-order treatment of diffusion terms in semi-lagrangian schemes. Commun. Comput. Phys. 8 (2010) 445–470. [Google Scholar]
- R. Ferretti, On the relationship between semi-Lagrangian and Lagrange-Galerkin schemes. Numer. Math. 124 (2013) 31–56. [CrossRef] [MathSciNet] [Google Scholar]
- E. Forest, Canonical integrators as tracking codes (1987) SSC-138. [Google Scholar]
- E. Forest and R. Ruth, Fourth-order symplectic integration. Physica D: Nonlinear Phenomena 43 (1990) 105–117. [CrossRef] [MathSciNet] [Google Scholar]
- P.E. Kloeden and E. Platen, Numerical solution of stochastic differential equations. Vol. 23 of Stoch. Model. Appl. Probab. Springer-Verlag, Berlin (1992). [Google Scholar]
- H. Kushner, Probability methods for approximations in stochastic control and for elliptic equations. Vol. 129 of Math. Sci. Eng. Academic Press, New York (1977). [Google Scholar]
- H. Kushner and P. Dupuis, Numerical methods for stochastic control problems in continuous time. Vol. 24 of Appl. Math., 2nd edn. Springer, New York (2001). [Google Scholar]
- P. Lesaint and P.A. Raviart, On a finite element method for solving the neutron transport equation. In Mathematical Aspects of Finite Elements in Partial Diffential Equations (1974) 89–145. [Google Scholar]
- J.-L. Menaldi, Some estimates for finite difference approximations. SIAM J. Control Optim. 27 (1989) 579–607. [CrossRef] [MathSciNet] [Google Scholar]
- G.N. Milstein, Weak approximation of solutions of systems of stochastic differential equations. Theory Probab. Appl. 30 (1986) 750–766. [Transl. from Teor. Veroyatnost. i Primenen. 30 (1985) 706–721.]. [CrossRef] [Google Scholar]
- G.N. Milstein and M.V. Tretyakov, Numerical solution of the Dirichlet problem for nonlinear parabolic equations by a probabilistic approach. IMA J. Numer. Anal. 21 (2001) 887–917. [CrossRef] [MathSciNet] [Google Scholar]
- K.W. Morton, A. Priestley and E. Süli, Stability of the Lagrange-Galerkin method with nonexact integration. RAIRO Modél. Math. Anal. Numér. 22 (1988) 625–653. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- É. Pardoux and D. Talay, Discretization and simulation of stochastic differential equations. Acta Appl. Math. 3 (1985) 23–47. [CrossRef] [MathSciNet] [Google Scholar]
- D.A.D. Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods. Vol. 69 of Math. Appl. Springer-Verlag, Berlin (2012). [Google Scholar]
- E. Platen, Zur zeitdiskreten approximation von itoprozessen. Diss. B. IMath, Akad. der Wiss. Der DDR, Berlin (1984). [Google Scholar]
- J.-M. Qiu and C.-W. Shu, Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: theoretical analysis and application to the Vlasov–Poisson system. J. Comput. Phys. 230 (2011) 8386–8409. [CrossRef] [MathSciNet] [Google Scholar]
- M. Restelli, L. Bonaventura and R. Sacco, A semi-Lagrangian discontinuous Galerkin method for scalar advection by incompressible flows. J. Comput. Phys. 216 (2006) 195–215. [CrossRef] [MathSciNet] [Google Scholar]
- R.D. Richtmyer and K.W. Morton, Difference methods for initial-value problems, 2nd edn. Interscience Tracts in Pure and Applied Mathematics, No. 4. Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney (1967). [Google Scholar]
- J.A. Rossmanith and D.C. Seal, A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov–Poisson equations. J. Comput. Phys. 230 (2011) 6203–6232. [CrossRef] [MathSciNet] [Google Scholar]
- D. Ruth, A canonical integration technique. Technical report (1983). [Google Scholar]
- C. Steiner, M. Mehrenberger and D. Bouche, A semi-Lagrangian discontinuous Galerkin approach. Technical Report (2013) hal-00852411. [Google Scholar]
- D. Talay, Efficient numerical schemes for the approximation of expectations of functionals of the solution of a SDE and applications. In Filtering and control of random processes (Paris, 1983). Vol. 61 of Lect. Notes Control Inform. Sci. Springer, Berlin (1984) 294–313. [Google Scholar]
- P. Wilmott, S. Howison and J. Dewynne, The mathematics of financial derivatives. A student introduction. Cambridge University Press, Cambridge (1995). [Google Scholar]
- Y. Yang and C.-W. Shu, Analysis of optimal superconvergence of discontinuous Galerkin method for linear hyperbolic equations. SIAM J. Numer. Anal. 50 (2012) 3110–3133. [CrossRef] [Google Scholar]
- H. Yoshida, Construction of higher order symplectic integrators. Phys. Lett. A 150 (1990) 262–268. [Google Scholar]
- H. Yoshida, Recent progress in the theory and application of symplectic integrators. Celest. Mech. Dyn. Astro. 56 (1993) 27–43. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.