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A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems

Assyr Abdulle , Gilles Vilmart
Numerische Mathematik, 2012, 121, pp.397-431. ⟨10.1007/s00211-011-0438-4⟩
Article dans une revue hal-00746826v1
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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

Assyr Abdulle , Gilles Vilmart
Comptes rendus hebdomadaires des séances de l'Académie des sciences, 2011, 349, pp.1041-1046. ⟨10.1016/j.crma.2011.09.005⟩
Article dans une revue hal-00772086v1
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Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete space-time analysis

Assyr Abdulle , Gilles Vilmart
Mathematical Models and Methods in Applied Sciences, 2012, 22 (6), 40 p. ⟨10.1142/S0218202512500029⟩
Article dans une revue hal-00746821v1
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Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

Assyr Abdulle , Yun Bai , Gilles Vilmart
Discrete and Continuous Dynamical Systems - Series S, 2015, 8 (1), pp.91-118. ⟨10.3934/dcdss.2015.8.91⟩
Article dans une revue hal-00811490v2
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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

Assyr Abdulle , Gilles Vilmart
Journal of Computational Physics, 2013, 242, pp.869-888. ⟨10.1016/j.jcp.2013.02.009⟩
Article dans une revue hal-00739757v2
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An optimization-based method for sign-changing elliptic PDEs

Assyr Abdulle , Simon Lemaire
ESAIM: Mathematical Modelling and Numerical Analysis, In press, ⟨10.1051/m2an/2024013⟩
Article dans une revue hal-04140542v2
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High order numerical approximation of the invariant measure of ergodic SDEs

Assyr Abdulle , Gilles Vilmart , Konstantinos Zygalakis
SIAM Journal on Numerical Analysis, 2014, 52 (4), pp.1600-1622. ⟨10.1137/130935616⟩
Article dans une revue hal-00858088v2
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Analysis of the finite element heterogeneous multiscale method for nonmonotone elliptic homogenization problems

Assyr Abdulle , Gilles Vilmart
Mathematics of Computation, 2014, 83 (286), pp.513-536. ⟨10.1090/S0025-5718-2013-02758-5⟩
Article dans une revue hal-00746811v2
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Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics

Assyr Abdulle , Gilles Vilmart , Konstantinos Zygalakis
SIAM Journal on Numerical Analysis, 2015, 53 (1), pp.1-16. ⟨10.1137/140962644⟩
Article dans une revue hal-00965354v2
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Weak second order explicit stabilized methods for stiff stochastic differential equations

Assyr Abdulle , Gilles Vilmart , Konstantinos Zygalakis
SIAM Journal on Scientific Computing, 2013, 35 (4), pp.1792-1814. ⟨10.1137/12088954X⟩
Article dans une revue hal-00739754v2
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Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems

Assyr Abdulle , Martin Huber , Gilles Vilmart
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2015, 13 (3), pp.916-952. ⟨10.1137/140975504⟩
Article dans une revue hal-01017106v3

FE heterogeneous multiscale method for long-time wave propagation

Assyr Abdulle , Marcus J. Grote , Christian Stohrer
Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2013, 351, pp.495-499. ⟨10.1016/j.crma.2013.06.002⟩
Article dans une revue hal-00968874v1
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Finite Element Heterogeneous Multiscale Method for the Wave Equation: Long-Time Effects

Assyr Abdulle , Marcus J. Grote , Christian Stohrer
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2014, 12 (3), pp.1230-1257. ⟨10.1137/13094195X⟩
Article dans une revue hal-01111169v1
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Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations

Assyr Abdulle , Gilles Vilmart , Konstantinos Zygalakis
BIT Numerical Mathematics, 2013, 53 (4), pp.827-840. ⟨10.1007/s10543-013-0430-8⟩
Article dans une revue hal-00739756v2
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An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems

Assyr Abdulle , Yun Bai , Gilles Vilmart
International Journal for Numerical Methods in Engineering, 2014, 99 (7), pp.469-486. ⟨10.1002/nme.4682⟩
Article dans une revue hal-00819565v1
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High weak order methods for stochastic differential equations based on modified equations

Assyr Abdulle , David Cohen , Gilles Vilmart , Konstantinos Zygalakis
SIAM Journal on Scientific Computing, 2012, 34 (3), pp.1800-1823. ⟨10.1137/110846609⟩
Article dans une revue hal-00746563v1