Numerical integrators based on modified differential equations. - Philippe Chartier; Ernst Hairer; Gilles Vilmart (Math. Comput., 2007)

Reducing round-off errors in rigid body dynamics. - Gilles Vilmart (J. Comput. Phys., 2008)

Algebraic Structures of B-series. - Philippe Chartier; Ernst Hairer; Gilles Vilmart (Found. Comput. Math., 2010)

A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems. - Assyr Abdulle; Gilles Vilmart (Numerische Mathematik, 2012)

High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations. - Assyr Abdulle; David Cohen; Gilles Vilmart; Konstantinos C. Zygalakis (SIAM J. Sci. Comput., 2012)

PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise. - Assyr Abdulle; Gilles Vilmart (J. Comput. Phys., 2013)

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations. - Assyr Abdulle; Gilles Vilmart; Konstantinos C. Zygalakis (SIAM J. Sci. Comput., 2013)

Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. - Assyr Abdulle; Gilles Vilmart (Math. Comput., 2014)

Multi-revolution composition methods for highly oscillatory differential equations. - Philippe Chartier; Joseba Makazaga; Ander Murua; Gilles Vilmart (Numerische Mathematik, 2014)

High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs. - Assyr Abdulle; Gilles Vilmart; Konstantinos C. Zygalakis (SIAM J. Numer. Anal., 2014)

Weak Second Order Multirevolution Composition Methods for Highly Oscillatory Stochastic Differential Equations with Additive or Multiplicative Noise. - Gilles Vilmart (SIAM J. Sci. Comput., 2014)

Linearized Numerical Homogenization Method for Nonlinear Monotone Parabolic Multiscale Problems. - Assyr Abdulle; Martin E. Huber; Gilles Vilmart (Multiscale Model. Simul., 2015)

Long Time Accuracy of Lie-Trotter Splitting Methods for Langevin Dynamics. - Assyr Abdulle; Gilles Vilmart; Konstantinos C. Zygalakis (SIAM J. Numer. Anal., 2015)

Postprocessed Integrators for the High Order Integration of Ergodic SDEs. - Gilles Vilmart (SIAM J. Sci. Comput., 2015)

High Order Integrator for Sampling the Invariant Distribution of a Class of Parabolic Stochastic PDEs with Additive Space-Time Noise. - Charles-Edouard Bréhier; Gilles Vilmart (SIAM J. Sci. Comput., 2016)

Optimal Explicit Stabilized Integrator of Weak Order 1 for Stiff and Ergodic Stochastic Differential Equations. - Assyr Abdulle; Ibrahim Almuslimani; Gilles Vilmart (SIAM/ASA J. Uncertain. Quantification, 2018)

Highly Oscillatory Problems with Time-Dependent Vanishing Frequency. - Philippe Chartier; Mohammed Lemou; Florian Méhats; Gilles Vilmart (SIAM J. Numer. Anal., 2019)

Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with oblique boundary conditions. - Guillaume Bertoli; Christophe Besse; Gilles Vilmart (CoRR, 2020)

A New Class of Uniformly Accurate Numerical Schemes for Highly Oscillatory Evolution Equations. - Philippe Chartier; Mohammed Lemou; Florian Méhats; Gilles Vilmart (Found. Comput. Math., 2020)

Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs. - Adrien Laurent; Gilles Vilmart (Math. Comput., 2020)

Strang Splitting Method for Semilinear Parabolic Problems With Inhomogeneous Boundary Conditions: A Correction Based on the Flow of the Nonlinearity. - Guillaume Bertoli; Gilles Vilmart (SIAM J. Sci. Comput., 2020)

Multirevolution Integrators for Differential Equations with Fast Stochastic Oscillations. - Adrien Laurent; Gilles Vilmart (SIAM J. Sci. Comput., 2020)

Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs. - Assyr Abdulle; Charles-Edouard Bréhier; Gilles Vilmart (CoRR, 2021)

Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions. - Guillaume Bertoli; Christophe Besse; Gilles Vilmart (Math. Comput., 2021)

Explicit Stabilized Integrators for Stiff Optimal Control Problems. - Ibrahim Almuslimani; Gilles Vilmart (SIAM J. Sci. Comput., 2021)

Order Conditions for Sampling the Invariant Measure of Ergodic Stochastic Differential Equations on Manifolds. - Adrien Laurent; Gilles Vilmart (Found. Comput. Math., 2022)

Drift-preserving numerical integrators for stochastic Poisson systems. - David Cohen; Gilles Vilmart (Int. J. Comput. Math., 2022)

Efficient Langevin sampling with position-dependent diffusion. - Eugen Bronasco; Benedict J. Leimkuhler; Dominic Phillips; Gilles Vilmart (CoRR, 2025)