, A multiscale finite element method for numerical homogenization . SIAM [Abd02] A. Abdulle. Fourth order Chebyshev methods with recurrence relation, Chapter Multiscale Model. Simul. SIAM J. Sci. Comput, vol.4, issue.236, pp.790-8122041, 2002.
, On a priori error analysis of fully discrete heterogeneous multiscale FEM. SIAM, Multiscale Model. Simul, vol.4, issue.2, pp.447-459, 2005.
, The finite element heterogeneous multiscale method: a computational strategy for multiscale pdes [Abd11] A. Abdulle. A priori and a posteriori error analysis for numerical homogenization: a unified framework, GAKUTO Int. Ser. Math. Sci. Appl. Ser. Contemp. Appl. Math. CAM, vol.31, issue.16, pp.135-184280, 2009.
, Discontinuous galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales, Abd13] A. Abdulle. Numerical homogenization methods. to appear in Springer, Encyclopedia of Applied and Computational Mathematics, pp.687-713, 2012.
, An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems, 2013.
, Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems, 2013.
, S-ROCK: Chebyshev Methods for Stiff Stochastic Differential Equations, SIAM Journal on Scientific Computing, vol.30, issue.2, pp.997-1014, 2008.
DOI : 10.1137/070679375
, High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations, SIAM Journal on Scientific Computing, vol.34, issue.3, pp.1800-1823, 2012.
DOI : 10.1137/110846609
URL : https://hal.archives-ouvertes.fr/hal-00746563
, Un r??sultat d'homog??n??isation pour une classe de probl??mes de diffusion non lin??aires stationnaires, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.4, issue.1, pp.1-28, 1982.
DOI : 10.5802/afst.572
URL : http://archive.numdam.org/article/AFST_1982_5_4_1_1_0.pdf
, Finite difference heterogeneous multi-scale method for homogenization problems, Journal of Computational Physics, vol.191, issue.1, pp.18-39, 2003.
DOI : 10.1016/S0021-9991(03)00303-6
, The heterogeneous multiscale method, Acta Numerica, vol.21, 2012.
DOI : 10.1017/S0962492912000025
URL : https://hal.archives-ouvertes.fr/hal-00746811
, S-ROCK methods for stiff Ito SDEs, Communications in Mathematical Sciences, vol.6, issue.4, pp.845-868, 2008.
DOI : 10.4310/CMS.2008.v6.n4.a3
, Second order Chebyshev methods based on orthogonal polynomials, Numerische Mathematik, vol.90, issue.1, pp.1-18, 2001.
DOI : 10.1007/s002110100292
, Stochastic differential equations: theory and applications, 1974.
, The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods Coupling heterogeneous multiscale FEM with Runge- Kutta methods for parabolic homogenization problems: a fully discrete spacetime analysis, C. R. Math. Acad. Sci. Paris Math. Models Methods Appl. Sci, vol.349, issue.40, pp.1041-10461250002, 2011.
, A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems, Numer. Math, vol.121, issue.3, pp.397-431, 2012.
, Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems, 2013.
, PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise, J. Comput. Phys, vol.242, pp.869-888, 2013.
, Weak second order explicit stabilized methods for stiff stochastic differential equations. to appear in SIAM, J. Sci. Comput, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00739754
, Long-run accuracy of numerical integrators for ergodic SDEs, 2013.
, Mean-square A-stable diagonally driftimplicit integrators with high order for stiff Ito systems of stochastic differential equations with noncommutative noise, 2013.
, Introduction to modelling of transport phenomena in porous media, Kluwer Academic, 1991.
, Improving on computation of homogenized coefficients in the periodic and quasi-periodic setting Numerical methods for strong solutions of stochastic differential equations: an overview, Netw. Heterog. Media Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci, vol.5, issue.1, pp.1-19, 2004.
, Symplectic integrators with processing: a general study, SIAM J. Sci. Comput, vol.21, pp.149-161, 1999.
DOI : 10.1137/s1064827598332497
, Partial differential equations, Lectures in Applied Mathematics, vol.III, 1964.
, Towards a Systematic Linear Stability Analysis of Numerical Methods for Systems of Stochastic Differential Equations, SIAM Journal on Numerical Analysis, vol.48, issue.1, pp.298-321, 2010.
DOI : 10.1137/090771843
, Asymptotic analysis for periodic structures, 1978.
, Homogénéisation de problèmes quasi-linéaires, pp.13-51, 1981.
, Correctors for the homogenization of the wave and heat equations, J. Math. Pures Appl, issue.93, pp.71197-231, 1992.
, Approximations of effective coefficients in stochastic homogenization, Annales de l?Institut Henri Poincare (B) Probability and Statistics, vol.40, issue.2, pp.153-165521, 2000.
DOI : 10.1016/j.anihpb.2003.07.003
, The mathematical theory of finite element methods The effective order of Runge-Kutta methods, of Texts in Applied Mathematics Proceedings of Conference on the Numerical Solution of Differential Equations, pp.133-139, 1969.
, An algebraic theory of integration methods, Mathematics of Computation, vol.26, issue.117, pp.79-106, 1972.
DOI : 10.1090/S0025-5718-1972-0305608-0
, Numerical methods for ordinary differential equations, 2008.
, On the theory of the analytic forms called trees, Phil. Magazine XIII, pp.172-176, 1857.
, Splitting methods with complex times for parabolic equations, BIT Numerical Mathematics, vol.150, issue.3, pp.487-508, 2009.
DOI : 10.1007/s10543-009-0235-y
URL : https://hal.archives-ouvertes.fr/hal-00777092
, Numerical stroboscopic averaging for ODEs and DAEs, Applied Numerical Mathematics, vol.61, issue.10, pp.611077-1095, 2011.
DOI : 10.1016/j.apnum.2011.06.007
URL : https://hal.archives-ouvertes.fr/hal-00777181
, An introduction to homogenization, of Oxford Lecture Series in Mathematics and its Applications, 1999.
, Upscaling of a class of nonlinear parabolic equations for the flow transport in heterogeneous porous media, Communications in Mathematical Sciences, vol.3, issue.4, pp.493-515, 2005.
DOI : 10.4310/CMS.2005.v3.n4.a2
, Two interacting Hopf algebras of trees. to appear in Adv, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00288313
, A substitution law for B-series vector fields, INRIA Report, issue.5498, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00070509
, Modified differential equations, ESAIM Proc, vol.21, pp.16-20, 2007.
, Numerical integrators based on modified differential equations The role of symplectic integrators in optimal control, Math. Comp. Optimal Control Appl. Methods, vol.76, issue.304, pp.1941-1953367, 2007.
, Algebraic Structures of B-series, Foundations of Computational Mathematics, vol.6, issue.4, pp.407-427, 2010.
DOI : 10.1007/s10208-010-9065-1
URL : https://hal.archives-ouvertes.fr/inria-00598369
, Basic error estimates for elliptic problems In Handbook of numerical analysis, II, Handb. Numer. Anal., II, pp.17-351, 1991.
, Approximate compositions of a near identity map by multi-revolution Runge-Kutta methods, Numerische Mathematik, vol.97, issue.4, pp.635-666, 2004.
DOI : 10.1007/s00211-004-0518-9
, Hopf Algebras, Renormalization and Noncommutative Geometry, Communications in Mathematical Physics, vol.199, issue.1, pp.203-242, 1998.
DOI : 10.1007/s002200050499
URL : http://arxiv.org/abs/hep-th/9808042
, Renormalization in Quantum Field Theory and the Riemann-Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem, Communications in Mathematical Physics, vol.210, issue.1, pp.249-273, 2000.
DOI : 10.1007/s002200050779
, Hopf Algebras, Cyclic Cohomology and the Transverse Index Theorem, Communications in Mathematical Physics, vol.198, issue.1, pp.199-246, 1998.
DOI : 10.1007/s002200050477
, Multi-revolution composition methods for highly oscillatory problems, 2013.
DOI : 10.1007/s00211-013-0602-0
URL : http://archive-ouverte.unige.ch/unige:41957
, A family of explicit multirevolution Runge- Kutta methods of order five, Analytic and numerical techniques in orbital dynamics (Spanish) Monogr. Real Acad. Ci. Exact. Fís.-Quím. Nat. Zaragoza, pp.45-54, 2002.
, On explicit multi-revolution Runge???Kutta schemes, Advances in Computational Mathematics, vol.4, issue.1-3, pp.1-3105, 2007.
DOI : 10.1007/s10444-004-7209-z
, Higher-Order Averaging, Formal Series and Numerical Integration I: B-series, Foundations of Computational Mathematics, vol.29, issue.6, pp.695-727, 2010.
DOI : 10.1007/s10208-010-9074-0
URL : https://hal.archives-ouvertes.fr/inria-00598357
, A formal series approach to averaging: Exponentially small error estimates, Discrete and Continuous Dynamical Systems, vol.32, issue.9, pp.3009-3027, 2012.
DOI : 10.3934/dcds.2012.32.3009
URL : https://hal.archives-ouvertes.fr/hal-00777178
, THE COMBINED EFFECT OF CURVED BOUNDARIES AND NUMERICAL INTEGRATION IN ISOPARAMETRIC FINITE ELEMENT METHODS, The mathematical foundations of the finite element method with applications to partial differential equations (Proc. Sympos, pp.409-474, 1972.
DOI : 10.1016/B978-0-12-068650-6.50020-4
, Approximation of parabolic equations, 2005.
, Analysis of the Multiscale Finite Element Method for Nonlinear and Random Homogenization Problems, SIAM Journal on Numerical Analysis, vol.46, issue.1, pp.260-27908, 2007.
DOI : 10.1137/060654207
, A Galerkin method for a nonlinear Dirichlet problem, Mathematics of Computation, vol.29, issue.131, pp.689-696, 1975.
DOI : 10.1090/S0025-5718-1975-0431747-2
, Weak Backward Error Analysis for SDEs, SIAM Journal on Numerical Analysis, vol.50, issue.3, pp.1735-1752, 2012.
DOI : 10.1137/110831544
URL : https://hal.archives-ouvertes.fr/hal-00589881
, Convergence of numerical schemes for the solution of parabolic stochastic partial differential equations Sulla convergenza degli integrali dell'energia per operatori ellittici del secondo ordine Diagonally drift-implicit runge?kutta methods of weak order one and two for itô sdes and stability analysis, Math. Comp. Boll. Un. Mat. Ital. Appl. Num. Math, vol.70, issue.59, pp.121-134391, 1973.
, Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations, Appl. Numer. Math, vol.59, pp.3-4582, 2009.
, Möbius functions, incidence algebras and power series representations, In Lecture Notes in Math, vol.1202, 1986.
, The heterogeneous multiscale methods, Commun. Math. Sci, vol.1, issue.1, pp.87-132, 2003.
, Heterogeneous multiscale methods: a review, Commun. Comput. Phys, vol.2, issue.3, pp.367-450, 2007.
, Analysis of the heterogeneous multiscale method for elliptic homogenization problems Efendiev and A. Pankov. Numerical homogenization of monotone elliptic operators, J. Amer. Math. Soc. Multiscale Model. Simul, vol.18, issue.21, pp.121-15662, 2003.
, Numerical Homogenization and Correctors for Nonlinear Elliptic Equations, SIAM Journal on Applied Mathematics, vol.65, issue.1, pp.43-68, 2004.
DOI : 10.1137/S0036139903424886
, Difference schemes for Hamiltonian formalism and symplectic geometry, J. Comp. Math, vol.4, pp.279-289, 1986.
, A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources, Journal of Computational Physics, vol.229, issue.20, pp.7625-7648, 2010.
DOI : 10.1016/j.jcp.2010.06.017
URL : https://hal.archives-ouvertes.fr/hal-00659668
, An analysis of finite element variational crimes for a nonlinear elliptic problem of a nonmonotone type, East-West J. Numer. Math, vol.1, issue.4, pp.267-285, 1993.
, Finite element solution of nonlinear elliptic problems, Numerische Mathematik, vol.10, issue.4, pp.451-475, 1987.
DOI : 10.1007/BF01396664
, Introduction to stochastic differential equations, 1988.
, Multilevel Monte Carlo path simulation, Operations Research, vol.56, issue.3, pp.607-617, 2008.
, An analytical framework for the numerical homogenization of monotone elliptic operators and quasiconvex energies, Multiscale Model. Simul, vol.5, issue.3, pp.996-1043, 2006.
, Reduction of the resonance error?Part 1: Approximation of homogenized coefficients, Math. Models Methods Appl. Sci, vol.21, issue.8, pp.1601-1630, 2011.
, Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations, ESAIM Math. Model. Numer. Anal, vol.46, issue.1, pp.1-38, 2012.
, On the energy exchange between resonant modes in nonlinear Schr??dinger equations, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.28, issue.1, pp.127-134, 2011.
DOI : 10.1016/j.anihpc.2010.11.004
, Stochastic stability of differential equations. Sijthoff and Noordhoff, The Netherlands, 1980.
, A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, vol.117, issue.4, pp.500-544, 1952.
DOI : 10.1113/jphysiol.1952.sp004764
, A-stability and stochastic mean-square stability Geometric Numerical Integration. Structure- Preserving Algorithms for Ordinary Differential Equations, Series in Computational Mathematics 31, pp.404-409, 2000.
, Solving Ordinary Differential Equations I. Nonstiff Problems, Series in Computational Mathematics 8, 1993.
DOI : 10.1007/978-3-662-12607-3
, Preprocessed discrete Moser???Veselov algorithm for the full dynamics of a rigid body, Journal of Physics A: Mathematical and General, vol.39, issue.42, pp.3913225-13235, 2006.
DOI : 10.1088/0305-4470/39/42/003
, ??ber die Butchergruppe und allgemeine Multi-Value Methoden, Computing, vol.11, issue.1, pp.1-15, 1974.
DOI : 10.1007/BF02268387
, Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics, vol.14, 1996.
, Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients, Mathematics of Computation, vol.68, issue.227, pp.913-943, 1999.
DOI : 10.1090/S0025-5718-99-01077-7
, Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations, SIAM Journal on Scientific Computing, vol.21, issue.2, pp.441-454, 1999.
DOI : 10.1137/S1064827598334599
, Homogenization of differential operators and integral functionals, 1994.
DOI : 10.1007/978-3-642-84659-5
, -ROCK methods for stochastic differential equations, Journal of Computational and Applied Mathematics, vol.242, pp.261-274, 2013.
DOI : 10.1016/j.cam.2012.10.026
URL : https://hal.archives-ouvertes.fr/hal-00002067
, An ODE-solver based on the method of averaging, Numer. Math, vol.53, issue.6, pp.621-652, 1988.
, Steady-state nonlinear heat conduction in composite materials using the method of fundamental solutions, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.33-40, pp.33-403122, 2008.
DOI : 10.1016/j.cma.2008.02.011
, Numerical solution of stochastic differential equations, 1992.
, Extrapolation Methods for the Weak Approximation of Ito Diffusions, SIAM Journal on Numerical Analysis, vol.32, issue.5, pp.1519-1534, 1995.
DOI : 10.1137/0732069
, The boundary value problems of mathematical physics, Applied Mathematical Sciences, vol.49, 1985.
, REDUCTION, RECONSTRUCTION, AND SKEW-PRODUCT DECOMPOSITION OF SYMMETRIC STOCHASTIC DIFFERENTIAL EQUATIONS, Stochastics and Dynamics, vol.09, issue.01, pp.1-46, 2009.
DOI : 10.1142/S0219493709002531
, Explicit difference schemes with time-variable steps for solving stiff systems of equations Random motion of a rigid body, Lions and E. Magenes. Problèmes aux limites non homogènes et applications Travaux et Recherches Mathématiques, pp.111-135201, 1968.
, A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit, SIAM Journal on Scientific Computing, vol.31, issue.1, pp.334-368, 2008.
DOI : 10.1137/07069479X
URL : https://hal.archives-ouvertes.fr/hal-00348594
, Runge-Kutta approximation of quasi-linear parabolic equations, Mathematics of Computation, vol.64, issue.210, pp.601-627, 1995.
DOI : 10.1090/S0025-5718-1995-1284670-0
, Simulating Hamiltonian Dynamics, Cambridge Monographs on Applied and Computational Mathematics, vol.14, 2004.
DOI : 10.1017/CBO9780511614118
URL : https://repozitorij.uni-lj.si/Dokument.php?id=39532
, Stochastic stabilization and destabilization, Systems Control Lett, vol.23, issue.4, pp.279-290, 1994.
, Continuous markov processes and stochastic equations, Rend. Circ. Mat. Palermo, vol.4, pp.48-90, 1955.
, Composition methods in the presence of small parameters, BIT, vol.35, pp.258-268, 1995.
, An operational method for the study of integration processes, Proc. Symp. Data Processing Weapons Research Establishment, pp.110-111, 1957.
, A Method of Second-Order Accuracy Integration of Stochastic Differential Equations, Theory of Probability & Its Applications, vol.23, issue.2, pp.396-401, 1978.
DOI : 10.1137/1123045
, Weak approximation of solutions of systems of stochastic differential equations, Theory Probab. Appl, vol.30, issue.4, pp.750-766, 1986.
DOI : 10.1007/978-94-015-8455-5_4
, A theorem on the order of convergence of mean-square approximations of solutions of systems of stochastic differential equations, Teor. Veroyatnost. i Primenen, vol.32, issue.4, pp.809-811, 1987.
, A new approach to the construction of multirevolution methods and their implementation, Applied Numerical Mathematics, vol.23, issue.2, pp.259-2741583, 1997.
DOI : 10.1016/S0168-9274(96)00055-4
, Order conditions for numerical integrators obtained by composing simpler integrators, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.357, issue.1754, pp.1079-1100, 1999.
DOI : 10.1098/rsta.1999.0365
, H-convergence In Topics in the mathematical modelling of composite materials, volume 31 of Progr, Nonlinear Differential Equations Appl. Birkhäuser Boston, pp.21-43, 1997.
, Discrete versions of some classical integrable systems and factorization of matrix polynomials, Communications in Mathematical Physics, vol.42, issue.4, pp.217-24387, 1991.
DOI : 10.1007/BF02352494
, Analysis of the heterogeneous multiscale method for parabolic homogenization problems, Mathematics of Computation, vol.76, issue.257, pp.153-177, 2007.
DOI : 10.1090/S0025-5718-06-01909-0
, Finite Element Computational Homogenization of Nonlinear Multiscale Materials in Magnetostatics, Proceedings of COMPUMAG-Sydney, 1. Static and quasi-static fields, 8. Material modelling, 2011.
DOI : 10.1109/TMAG.2011.2174210
, Stochastic differential equations. Universitext, 2003.
, Numerical solution of highly oscillatory ordinary differential equations, Acta numerica, pp.437-483, 1997.
DOI : 10.1007/BF01600630
, High-order weak approximation of ito diffusions by markov chains, Probab. Engrg. Inform. Sci, vol.6, pp.391-408, 1992.
, Multiscale methods Averaging and homogenization, Texts in Applied Mathematics, vol.53, 2008.
, Mean-square stability of second-order Runge???Kutta methods for multi-dimensional linear stochastic differential systems, Journal of Computational and Applied Mathematics, vol.219, issue.1, pp.170-197, 2008.
DOI : 10.1016/j.cam.2007.07.019
, The Fokker-Planck equation, 1989.
, Runge-Kutta methods for the numerical solution of stochastic diifferential equations, Diss. TU Darmstadt. Shaker Verlag, 2003.
, Second order Runge-Kutta methods for Itô stochastic differential equations, SIAM J. Numer. Anal, vol.47, issue.3, pp.1713-1738, 2009.
, A canonical integration technique, IEEE Trans. Nuclear Science, NS, vol.30, pp.2669-2671, 1983.
, An observation concerning Ritz-Galerkin methods with indefinite bilinear forms, Math. Comp, vol.28, pp.959-962, 1974.
, Modified equations for stochastic differential equations, BIT, vol.46, issue.1, pp.111-125, 2006.
, Stability Analysis of Numerical Schemes for Stochastic Differential Equations, SIAM Journal on Numerical Analysis, vol.33, issue.6, pp.2254-2267, 1996.
DOI : 10.1137/S0036142992228409
, Mean-square stability of numerical schemes for stochastic differential systems, Vietnam J. Math, vol.30, pp.551-560, 2002.
, Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche 571-597; errata, ibid RKC: an explicit solver for parabolic PDEs, Ann. Scuola Norm. Sup. Pisa J. Comput. Appl. Math, vol.22, issue.88, pp.673316-326, 1968.
, Efficient numerical schemes for the approximation of expectations of functionals of the solution of a SDE and applications, Lecture Notes in Control and Inform. Sci, vol.61, pp.294-313, 1984.
, Mean-square stability of second-order Runge-Kutta methods for stochastic differential equations, J. Comput. Appl. Math, vol.175, issue.2, pp.355-367, 2005.
, Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastic Anal Weak second order conditions for stochastic Runge- Kutta methods, Appl. SIAM J. Sci. Comput, vol.8, issue.242, pp.483-509507, 1990.
URL : https://hal.archives-ouvertes.fr/inria-00075490
, Convergence properties of the rungekutta-chebyshev method, Numer. Math, vol.57, pp.157-178, 1990.
, Étude d'intégrateurs géométriques pour des équations différentielles, 2008.
, Reducing round-off errors in rigid body dynamics, J. Comput. Phys, vol.227, issue.15, pp.7083-7088, 2008.
, Rigid body dynamics, Encyclopedia of Applied and Computational Mathematics, 2013.
, On the Internal Stability of Explicit,m-Stage Runge-Kutta Methods for Largem-Values, ZAMM - Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.3, issue.10, pp.479-485, 1980.
DOI : 10.1002/zamm.19800601005
, RKC time-stepping for advection???diffusion???reaction problems, Journal of Computational Physics, vol.201, issue.1, pp.61-79, 2004.
DOI : 10.1016/j.jcp.2004.05.002
, An introduction to stochastic partial differential equations, Lecture Notes in Mathematics, vol.1180, pp.265-439, 1986.
DOI : 10.1007/BFb0074920
, Temperature-dependent thermal diffusivity of the Earth???s crust and implications for magmatism, Nature, vol.47, issue.7236, pp.319-321, 2009.
DOI : 10.1038/nature07818
, Partitioned Runge-Kutta-Chebyshev methods for diffusion-advectionreaction problems, SIAM J. Sci. Comput, vol.33, issue.4, pp.1707-1725, 2011.
, On the existence and the applications of modified equations for stochastic differential equations An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems, SIAM J. Sci. Comput, vol.33, issue.1, pp.102-130, 2011.
, Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems, Discrete and Continuous Dynamical Systems - Series S, vol.8, issue.1, 2013.
DOI : 10.3934/dcdss.2015.8.91
URL : https://hal.archives-ouvertes.fr/hal-00811490
, High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations, SIAM Journal on Scientific Computing, vol.34, issue.3, pp.1800-1823, 2012.
DOI : 10.1137/110846609
URL : https://hal.archives-ouvertes.fr/hal-00746563
, Fully-discrete space-time analysis for parabolic nonlinear monotone single scale and multiscale problems, 2013.
, The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods, Comptes Rendus Mathematique, vol.349, issue.19-20, pp.19-201041, 2011.
DOI : 10.1016/j.crma.2011.09.005
URL : https://hal.archives-ouvertes.fr/hal-00772086
, Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete spacetime analysis Abdulle and G. Vilmart. A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems, Math. Models Methods Appl. Sci. Numer. Math, vol.22, issue.1213, pp.1250002397-431, 2012.
, Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems, 2013.
, PIROCK: a swiss-knife partitioned implicitexplicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusionadvection-reaction problems with or without noise, J. Comput. Phys, vol.242, pp.869-888, 2013.
, Weak second order explicit stabilized methods for stiff stochastic differential equations. to appear in SIAM, J. Sci. Comput, 2012.
DOI : 10.1137/12088954x
URL : https://hal.archives-ouvertes.fr/hal-00739754
, Long-run accuracy of numerical integrators for ergodic SDEs In preparation, 2013. Personal bibliography Mean-square A-stable diagonally drift-implicit integrators with high order for stiff Ito systems of stochastic differential equations with noncommutative noise, 2013.
, Splitting methods with complex times for parabolic equations, BIT Numerical Mathematics, vol.150, issue.3, pp.487-508, 2009.
DOI : 10.1007/s10543-009-0235-y
URL : https://hal.archives-ouvertes.fr/hal-00777092
, A substitution law for B-series vector fields, INRIA Report, issue.5498, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00070509
, Modified differential equations, ESAIM: Proceedings, vol.21, pp.16-20, 2007.
DOI : 10.1051/proc:072102
URL : https://hal.archives-ouvertes.fr/hal-00847919
, Numerical integrators based on modified differential equations The role of symplectic integrators in optimal control, Math. Comp. Optimal Control Appl. Methods, vol.76, issue.304, pp.1941-1953367, 2007.
, Algebraic Structures of B-series, Foundations of Computational Mathematics, vol.6, issue.4, pp.407-427, 2010.
DOI : 10.1007/s10208-010-9065-1
URL : https://hal.archives-ouvertes.fr/inria-00598369
, Multi-revolution composition methods for highly oscillatory problems, 2013.
DOI : 10.1007/s00211-013-0602-0
URL : http://archive-ouverte.unige.ch/unige:41957
, Preprocessed discrete Moser???Veselov algorithm for the full dynamics of a rigid body, Journal of Physics A: Mathematical and General, vol.39, issue.42, pp.3913225-13235, 2006.
DOI : 10.1088/0305-4470/39/42/003
, Étude d'intégrateurs géométriques pour des équations différentielles, 2008.
, Reducing round-off errors in rigid body dynamics, J. Comput. Phys, vol.227, issue.15, pp.7083-7088, 2008.
, Rigid body dynamics, Encyclopedia of Applied and Computational Mathematics, 2013.