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1

A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

Abdulle, Assyr, Rosilho de Souza, Giacomo

Journal:

ESAIM Mathematical Modelling and Numerical Analysis

Year:

2019

Language:

english

File:

PDF, 1.85 MB

english, 2019

2

200 years of least squares method

Assyr Abdulle, Gerhard Wanner

Journal:

Elemente der Mathematik

Year:

2002

Language:

english

File:

PDF, 727 KB

english, 2002

3

Multilevel Monte Carlo Methods for Stochastic Elliptic Multiscale PDEs

Abdulle, Assyr, Barth, Andrea, Schwab, Christoph

Journal:

Multiscale Modeling and Simulation

Year:

2013

Language:

english

File:

PDF, 595 KB

english, 2013

4

Multiscale method based on discontinuous Galerkin methods for homogenization problems

Journal:

Comptes Rendus Mathematique

Year:

2008

File:

PDF, 140 KB

2008

5

Finite difference heterogeneous multi-scale method for homogenization problems

Assyr Abdulle, Weinan E

Journal:

Journal of Computational Physics

Year:

2003

Language:

english

File:

PDF, 397 KB

english, 2003

6

Second order Chebyshev methods based on orthogonal polynomials

Assyr Abdulle, Alexei A. Medovikov

Journal:

Numerische Mathematik

Year:

2001

Language:

english

File:

PDF, 335 KB

english, 2001

7

Fourth Order Chebyshev Methods with Recurrence Relation

Journal:

SIAM Journal on Scientific Computing

Year:

2002

Language:

english

File:

PDF, 327 KB

english, 2002

8

Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

Abdulle, Assyr, Vilmart, Gilles

Journal:

Mathematics of Computation

Year:

2013

Language:

english

File:

PDF, 412 KB

english, 2013

9

A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method

Abdulle, Assyr, Nonnenmacher, Achim

Journal:

Numerical Methods for Partial Differential Equations

Year:

2013

Language:

english

File:

PDF, 3.98 MB

english, 2013

10

High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations

Abdulle, Assyr, Cohen, David, Vilmart, Gilles, Zygalakis, Konstantinos C.

Journal:

SIAM Journal on Scientific Computing

Year:

2012

Language:

english

File:

PDF, 599 KB

english, 2012

11

The heterogeneous multiscale method

Abdulle, Assyr, Weinan, E, Engquist, Björn, Vanden-Eijnden, Eric

Journal:

Year:

2012

Language:

english

File:

PDF, 3.57 MB

english, 2012

12

[Lecture Notes in Computational Science and Engineering] Numerical Mathematics and Advanced Applications - ENUMATH 2013 Volume 103 || Modified Pressure-Correction Projection Methods: Open Boundary and Variable Time Stepping

Abdulle, Assyr, Deparis, Simone, Kressner, Daniel, Nobile, Fabio, Picasso, Marco

Year:

2015

Language:

english

File:

PDF, 257 KB

english, 2015

13

Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales

Journal:

Mathematics of Computation

Year:

2011

Language:

english

File:

PDF, 410 KB

english, 2011

14

On heterogeneous coupling of multiscale methods for problems with and without scale separation

Abdulle, Assyr, Jecker, Orane

Journal:

Research in the Mathematical Sciences

Year:

2017

Language:

english

File:

PDF, 1.73 MB

english, 2017

15

Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems

Abdulle, Assyr, Arjmand, Doghonay, Paganoni, Edoardo

Journal:

Comptes Rendus Mathematique

Year:

2019

Language:

english

File:

PDF, 534 KB

english, 2019

16

A Bayesian Numerical Homogenization Method for Elliptic Multiscale Inverse Problems

Abdulle, Assyr, Blasio, Andrea Di

Journal:

SIAM/ASA Journal on Uncertainty Quantification

Year:

2020

File:

PDF, 21.18 MB

2020

17

Ensemble Kalman Filter for Multiscale Inverse Problems

Abdulle, Assyr, Garegnani, Giacomo, Zanoni, Andrea

Journal:

Multiscale Modeling and Simulation

Year:

2020

File:

PDF, 4.23 MB

2020

18

A short and versatile finite element multiscale code for homogenization problems

Assyr Abdulle, Achim Nonnenmacher

Journal:

Computer Methods in Applied Mechanics and Engineering

Year:

2009

Language:

english

File:

PDF, 3.13 MB

english, 2009

19

Stabilized methods for stiff stochastic systems

Assyr Abdulle, Stéphane Cirilli

Journal:

Comptes Rendus Mathematique

Year:

2007

File:

PDF, 308 KB

2007

20

A posteriori error analysis of the heterogeneous multiscale method for homogenization problems

Assyr Abdulle, Achim Nonnenmacher

Journal:

Comptes Rendus Mathematique

Year:

2009

File:

PDF, 189 KB

2009

21

Solving Multi-Scale problems with heterogeneous finite difference methods

Journal:

Year:

2003

Language:

english

File:

PDF, 150 KB

english, 2003

22

Solving Diffusion Problems on Rough Surfaces with a Hierarchical Multiscale FEM

Journal:

Year:

2004

Language:

english

File:

PDF, 142 KB

english, 2004

23

Erratum to “A short and versatile finite element multiscale code for homogenization problems” [Comput. Methods Appl. Mech. Engrg. 198 (2009) 2839–2859]

Assyr Abdulle, Achim Nonnenmacher

Journal:

Computer Methods in Applied Mechanics and Engineering

Year:

2010

Language:

english

File:

PDF, 90 KB

english, 2010

24

On Roots and Error Constants of Optimal Stability Polynomials

Journal:

BIT Numerical Mathematics

Year:

2000

Language:

english

File:

PDF, 1.30 MB

english, 2000

25

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

Assyr Abdulle, Gilles Vilmart

Journal:

Numerische Mathematik

Year:

2012

Language:

english

File:

PDF, 629 KB

english, 2012

26

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

Journal:

Comptes Rendus Mathematique

Year:

2011

Language:

french

File:

PDF, 165 KB

french, 2011

27

S-ROCK: Chebyshev Methods for Stiff Stochastic Differential Equations

Abdulle, Assyr, Cirilli, Stephane

Journal:

SIAM Journal on Scientific Computing

Year:

2008

Language:

english

File:

PDF, 1.94 MB

english, 2008

28

Numerical Methods for Multilattices

Abdulle, Assyr, Lin, Ping, Shapeev, Alexander V.

Journal:

Multiscale Modeling and Simulation

Year:

2012

Language:

english

File:

PDF, 441 KB

english, 2012

29

On A Priori Error Analysis of Fully Discrete Heterogeneous Multiscale FEM

Journal:

Multiscale Modeling and Simulation

Year:

2005

Language:

english

File:

PDF, 203 KB

english, 2005

30

Finite Element Heterogeneous Multiscale Methods with Near Optimal Computational Complexity

Abdulle, Assyr, Engquist, Bjorn

Journal:

Multiscale Modeling and Simulation

Year:

2008

Language:

english

File:

PDF, 1.45 MB

english, 2008

31

Heterogeneous Multiscale FEM for Diffusion Problems on Rough Surfaces

Abdulle, Assyr, Schwab, Christoph

Journal:

Multiscale Modeling and Simulation

Year:

2005

Language:

english

File:

PDF, 1.57 MB

english, 2005

32

Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems

Assyr Abdulle, Yun Bai

Journal:

Journal of Computational Physics

Year:

2012

Language:

english

File:

PDF, 1.17 MB

english, 2012

33

Stabilized multilevel Monte Carlo method for stiff stochastic differential equations

Abdulle, Assyr, Blumenthal, Adrian

Journal:

Journal of Computational Physics

Year:

2013

Language:

english

File:

PDF, 1.28 MB

english, 2013

34

FE heterogeneous multiscale method for long-time wave propagation

Abdulle, Assyr, Grote, Marcus J., Stohrer, Christian

Journal:

Comptes Rendus Mathematique

Year:

2013

Language:

french

File:

PDF, 258 KB

french, 2013

35

Adaptive reduced basis finite element heterogeneous multiscale method

Abdulle, Assyr, Bai, Yun

Journal:

Computer Methods in Applied Mechanics and Engineering

Year:

2013

Language:

english

File:

PDF, 1.97 MB

english, 2013

36

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

Journal:

Journal of Computational Physics

Year:

2013

Language:

english

File:

PDF, 3.61 MB

english, 2013

37

High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs

Abdulle, Assyr, Vilmart, Gilles, Zygalakis, Konstantinos C.

Journal:

SIAM Journal on Numerical Analysis

Year:

2014

Language:

english

File:

PDF, 925 KB

english, 2014

38

Finite Element Heterogeneous Multiscale Method for the Wave Equation

Abdulle, Assyr, Grote, Marcus J.

Journal:

Multiscale Modeling and Simulation

Year:

2011

Language:

english

File:

PDF, 579 KB

english, 2011

39

A Priori and A Posteriori $W^{1,\infty}$ Error Analysis of a QC Method for Complex Lattices

Abdulle, Assyr, Lin, Ping, Shapeev, Alexander V.

Journal:

SIAM Journal on Numerical Analysis

Year:

2013

Language:

english

File:

PDF, 681 KB

english, 2013

40

Finite Element Heterogeneous Multiscale Method for the Wave Equation: Long-Time Effects

Abdulle, Assyr, Grote, Marcus J., Stohrer, Christian

Journal:

Multiscale Modeling and Simulation

Year:

2014

Language:

english

File:

PDF, 1.14 MB

english, 2014

41

[Lecture Notes in Computational Science and Engineering] Numerical Mathematics and Advanced Applications - ENUMATH 2013 Volume 103 ||

Abdulle, Assyr, Deparis, Simone, Kressner, Daniel, Nobile, Fabio, Picasso, Marco

Year:

2015

Language:

english

File:

PDF, 19.73 MB

english, 2015

42

[Lecture Notes in Computational Science and Engineering] Numerical Mathematics and Advanced Applications - ENUMATH 2013 Volume 103 || Inverse Problem of a Boundary Function Recovery by Observation Data for the Shallow Water Model

Abdulle, Assyr, Deparis, Simone, Kressner, Daniel, Nobile, Fabio, Picasso, Marco

Year:

2015

Language:

english

File:

PDF, 255 KB

english, 2015

43

[Lecture Notes in Computational Science and Engineering] Numerical Mathematics and Advanced Applications - ENUMATH 2013 Volume 103 || Stability of Explicit Runge-Kutta Methods for High Order Finite Element Approximation of Linear Parabolic Equations

Abdulle, Assyr, Deparis, Simone, Kressner, Daniel, Nobile, Fabio, Picasso, Marco

Year:

2015

Language:

english

File:

PDF, 191 KB

english, 2015

44

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

Abdulle, Assyr, Vilmart, Gilles, Zygalakis, Konstantinos C.

Journal:

SIAM Journal on Scientific Computing

Year:

2013

Language:

english

File:

PDF, 1.11 MB

english, 2013

45

[Lecture Notes in Computational Science and Engineering] Numerical Mathematics and Advanced Applications - ENUMATH 2013 Volume 103 || Reduced Order Optimal Control Using Proper Orthogonal Decomposition Sensitivities

Abdulle, Assyr, Deparis, Simone, Kressner, Daniel, Nobile, Fabio, Picasso, Marco

Year:

2015

Language:

english

File:

PDF, 223 KB

english, 2015

46

[Lecture Notes in Computational Science and Engineering] Numerical Mathematics and Advanced Applications - ENUMATH 2013 Volume 103 || Reliable a Posteriori Error Estimation for Plane Problems in Cosserat Elasticity

Abdulle, Assyr, Deparis, Simone, Kressner, Daniel, Nobile, Fabio, Picasso, Marco

Year:

2015

Language:

english

File:

PDF, 178 KB

english, 2015

47

[Lecture Notes in Computational Science and Engineering] Numerical Mathematics and Advanced Applications - ENUMATH 2013 Volume 103 || Numerical Modelling of Viscoelastic Fluid-Structure Interaction and Its Application for a Valveless Micropump

Abdulle, Assyr, Deparis, Simone, Kressner, Daniel, Nobile, Fabio, Picasso, Marco

Year:

2015

Language:

english

File:

PDF, 531 KB

english, 2015

48

COUPLING HETEROGENEOUS MULTISCALE FEM WITH RUNGE–KUTTA METHODS FOR PARABOLIC HOMOGENIZATION PROBLEMS: A FULLY DISCRETE SPACETIME ANALYSIS

ABDULLE, ASSYR, VILMART, GILLES

Journal:

Mathematical Models and Methods in Applied Sciences

Year:

2012

Language:

english

File:

PDF, 685 KB

english, 2012

49

A Petrov–Galerkin reduced basis approximation of the Stokes equation in parameterized geometries

Abdulle, Assyr, Budáč, Ondrej

Journal:

Comptes Rendus Mathematique

Year:

2015

File:

PDF, 500 KB

2015

50

[Lecture Notes in Computational Science and Engineering] Numerical Mathematics and Advanced Applications - ENUMATH 2013 Volume 103 || Solving a Maxwell Interface Problem by a Local L 2 Projected C 0Finite Element Method

Abdulle, Assyr, Deparis, Simone, Kressner, Daniel, Nobile, Fabio, Picasso, Marco

Year:

2015

Language:

english

File:

PDF, 153 KB

english, 2015

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