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Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations Abdulle, Assyr; Pavliotis, Grigorios A.; Vilmart, Gilles 2019
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Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations Abdulle, Assyr; Almuslimani, Ibrahim; Vilmart, Gilles 2018
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Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems Abdulle, Assyr; Bai, Yun; Vilmart, Gilles 2015
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Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 2015
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Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems Abdulle, Assyr; Huber, Martin; Vilmart, Gilles 2015
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Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems Abdulle, Assyr; Vilmart, Gilles 2014
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High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 2014
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An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems Abdulle, Assyr; Bai, Yun; Vilmart, Gilles 2014
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PIROCK: A swiss-knife partitioned implicit–explicit orthogonal Runge–Kutta Chebyshev integrator for stiff diffusion–advection–reaction problems with or without noise Abdulle, Assyr; Vilmart, Gilles 2013
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Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 2013
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Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 2013
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A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems Abdulle, Assyr; Vilmart, Gilles 2012
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Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete space-time analysis Abdulle, Assyr; Vilmart, Gilles 2012
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High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C. 2012
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The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods Abdulle, Assyr; Vilmart, Gilles 2011
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S-Rock: Chebyshev methods for stiff stochastic differential equations Abdulle, Assyr; Cirilli, Stephane 2008
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200 years of least squares method Abdulle, Assyr; Wanner, Gerhard 2002
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Fourth Order Chebyshev Methods with Recurrence Relation Abdulle, Assyr 2002
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Second order Chebyshev methods based on orthogonal polynomials Abdulle, Assyr; Medovikov, Alexei A. 2001
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On roots and error constants of optimal stability polynomials Abdulle, Assyr 2000