ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)

Recent Progress in Computational and Applied PDES

Wu Yu-jiang and Yang Zhong-hua
Recent Progress in Computational and Applied PDES 383 (2002)
https://doi.org/10.1007/978-1-4615-0113-8_26

K. Kemenov and S. Menon
(2002)
https://doi.org/10.2514/6.2002-287

Stability of Galerkin and Inertial Algorithms with variable time step size

Yinnian He and Kaitai Li
Journal of Computational and Applied Mathematics 146 (2) 213 (2002)
https://doi.org/10.1016/S0377-0427(02)00354-0

Stabilized finite element approximation of transient incompressible flows using orthogonal subscales

Ramon Codina
Computer Methods in Applied Mechanics and Engineering 191 (39-40) 4295 (2002)
https://doi.org/10.1016/S0045-7825(02)00337-7

Postprocessing Fourier spectral methods: The case of smooth solutions

Bosco García-Archilla, Julia Novo and Edriss S. Titi
Applied Numerical Mathematics 43 (3) 191 (2002)
https://doi.org/10.1016/S0168-9274(01)00134-9

DPIV/T-driven convective heat transfer simulation

X. Ma, G.E. Karniadakis, H. Park and M. Gharib
International Journal of Heat and Mass Transfer 45 (17) 3517 (2002)
https://doi.org/10.1016/S0017-9310(02)00071-6

A. Armaou and P.D. Christofides
2 2310 (2002)
https://doi.org/10.1109/CDC.2002.1184877

A nonlinear galerkin mixed element method and a posteriori error estimator for the stationary navier-stokes equations

Luo Zhen-dong and Zhu Jiang
Applied Mathematics and Mechanics 23 (10) 1194 (2002)
https://doi.org/10.1007/BF02437668

Dynamic optimization of dissipative PDE systems using nonlinear order reduction

Antonios Armaou and Panagiotis D. Christofides
Chemical Engineering Science 57 (24) 5083 (2002)
https://doi.org/10.1016/S0009-2509(02)00419-0

The Energy Operator and New Scaling Relations for the Incompressible Navier--Stokes Equations

Paul F. Batcho
SIAM Journal on Applied Mathematics 62 (1) 70 (2001)
https://doi.org/10.1137/S0036139999354121

Accurate Computations on Inertial Manifolds

M. S. Jolly, R. Rosa and R. Temam
SIAM Journal on Scientific Computing 22 (6) 2216 (2001)
https://doi.org/10.1137/S1064827599351738

A Nonlinear Galerkin Method for the Shallow-Water Equations on Periodic Domains

Saulo R.M. Barros and José W. Cárdenas
Journal of Computational Physics 172 (2) 592 (2001)
https://doi.org/10.1006/jcph.2001.6843

Two-grid finite-element schemes for the transient Navier-Stokes problem

Vivette Girault and Jacques-Louis Lions
ESAIM: Mathematical Modelling and Numerical Analysis 35 (5) 945 (2001)
https://doi.org/10.1051/m2an:2001145

Subgrid stabilization of Galerkin approximations of linear contraction semi-groups of classC0 in Hilbert spaces

Jean-Luc Guermond
Numerical Methods for Partial Differential Equations 17 (1) 1 (2001)
https://doi.org/10.1002/1098-2426(200101)17:1<1::AID-NUM1>3.0.CO;2-1

A microscopic derivation of the equilibrium energy density spectrum for barotropic turbulence on a sphere

Chjan C. Lim
Physica A: Statistical Mechanics and its Applications 294 (3-4) 375 (2001)
https://doi.org/10.1016/S0378-4371(01)00029-2

A multilevel method applied in the nonhomogeneous direction of the channel flow problem

F. Bouchon and F. Jauberteau
Applied Numerical Mathematics 36 (1) 1 (2001)
https://doi.org/10.1016/S0168-9274(99)00043-4

The Generalized Nonlinear Galerkin Method Applied to Hydrodynamics of the Open Sea

B. DI MARTINO and P. ORENGA
International Journal of Computational Fluid Dynamics 14 (4) 305 (2001)
https://doi.org/10.1080/10618560108940731

A ladder inequality for the Navier-Stokes equation

Igor Kukavica
Nonlinearity 13 (3) 639 (2000)
https://doi.org/10.1088/0951-7715/13/3/307

Limiting Behavior for an Iterated Viscosity

Ciprian Foias, Michael S. Jolly and Oscar P. Manley
ESAIM: Mathematical Modelling and Numerical Analysis 34 (2) 353 (2000)
https://doi.org/10.1051/m2an:2000145

Stability and convergence for the reform postprocessing Galerkin method

He Yinnian and R.M.M. Mattheij
Nonlinear Analysis: Real World Applications 1 (4) 517 (2000)
https://doi.org/10.1016/S0362-546X(99)00283-7

Resolution of a stochastic weakly damped nonlinear Schrödinger equation by a multilevel numerical method

Guy Moebs and Roger Temam
Journal of the Optical Society of America A 17 (10) 1870 (2000)
https://doi.org/10.1364/JOSAA.17.001870

An Adaptive Multi-level method for Convection Diffusion Problems

Martine Marion and Adeline Mollard
ESAIM: Mathematical Modelling and Numerical Analysis 34 (2) 439 (2000)
https://doi.org/10.1051/m2an:2000150

A Spectral Element Method for the Navier--Stokes Equations with Improved Accuracy

Javier de Frutos and Julia Novo
SIAM Journal on Numerical Analysis 38 (3) 799 (2000)
https://doi.org/10.1137/S0036142999351984

LOCALIZATION AND APPROXIMATION OF ATTRACTORS FOR THE KURAMOTO-SIVASHINSKY EQUATIONS

Yujiang Wu and Benyu Guo
Acta Mathematica Scientia 20 (2) 145 (2000)
https://doi.org/10.1016/S0252-9602(17)30551-9

Parallel Solution of Partial Differential Equations

Amir Averbuch, Ludimila Ioffe, Moshe Israeli and Lev Vozovoi
The IMA Volumes in Mathematics and its Applications, Parallel Solution of Partial Differential Equations 120 123 (2000)
https://doi.org/10.1007/978-1-4612-1176-1_6

A simple postrocess procedure for Galerkin method

Hou Yanren and Li Kaitai
Applied Mathematics and Mechanics 21 (1) 79 (2000)
https://doi.org/10.1007/BF02458543

Direct and Large-Eddy Simulation III

F. Bouchon and T. Dubois
ERCOFTAC Series, Direct and Large-Eddy Simulation III 7 275 (1999)
https://doi.org/10.1007/978-94-015-9285-7_23

Resolution to a three-dimensional physical oceanographic problem using the non-linear Galerkin method

Bernard Di Martino and Pierre Orenga
International Journal for Numerical Methods in Fluids 30 (5) 577 (1999)
https://doi.org/10.1002/(SICI)1097-0363(19990715)30:5<577::AID-FLD858>3.0.CO;2-T

Postprocessing the Galerkin Method: The Finite-Element Case

Bosco GarcÍa-Archilla and Edriss S. Titi
SIAM Journal on Numerical Analysis 37 (2) 470 (1999)
https://doi.org/10.1137/S0036142998335893

Industrial and Environmental Applications of Direct and Large-Eddy Simulation

Kunt Atalık and Akın Tezel
Lecture Notes in Physics, Industrial and Environmental Applications of Direct and Large-Eddy Simulation 529 230 (1999)
https://doi.org/10.1007/BFb0106106

An approximate inertial manifolds approach to postprocessing the Galerkin method for the Navier-Stokes equations

Bosco García-Archilla, Julia Novo and Edriss Titi
Mathematics of Computation 68 (227) 893 (1999)
https://doi.org/10.1090/S0025-5718-99-01057-1

Postprocessing the Galerkin Method: a Novel Approach to Approximate Inertial Manifolds

Bosco García-Archilla, Julia Novo and Edriss S. Titi
SIAM Journal on Numerical Analysis 35 (3) 941 (1998)
https://doi.org/10.1137/S0036142995296096

The Additive Turbulent Decomposition for the Two-Dimensional Incompressible Navier--Stokes Equations: Convergence Theorems and Error Estimates

Peter Perry, Russell M. Brown and Zhongwei Shen
SIAM Journal on Applied Mathematics 59 (1) 139 (1998)
https://doi.org/10.1137/S0036139996311618

Incremental unknowns, multilevel methods and the numerical simulation of turbulence

T. Dubois, F. Jauberteau and R. Temam
Computer Methods in Applied Mechanics and Engineering 159 (1-2) 123 (1998)
https://doi.org/10.1016/S0045-7825(98)80106-0

Nonlinear Galerkin methods based on the concept of determining modes for the magnetohydrodynamic equations

Olaf Schmidtmann, Fred Feudel and Norbert Seehafer
Journal of Physics A: Mathematical and General 31 (34) 7141 (1998)
https://doi.org/10.1088/0305-4470/31/34/016

The spectral method for the flow between two concentric rotating spheres, part II: The full discrete nonlinear Legendre-Galerkin method

Weibing Feng and Kaitai Li
Communications in Nonlinear Science and Numerical Simulation 3 (4) 211 (1998)
https://doi.org/10.1016/S1007-5704(98)90036-3

Explicit construction of integral manifolds with exponential tracking

V.V. Chepyzhov and A.Yu. Goritsky
Applicable Analysis 71 (1-4) 237 (1998)
https://doi.org/10.1080/00036819908840715

Order Reduction of Nonlinear Dynamic Models for Distributed Reacting Systems

S.Y. Shvartsman, R. Rico-Martínez, E.S. Titi, et al.
IFAC Proceedings Volumes 31 (11) 637 (1998)
https://doi.org/10.1016/S1474-6670(17)44998-6

A multilevel method for the resolution of a stochastic weakly damped nonlinear Schrödinger equation

Guy Moebs
Applied Numerical Mathematics 26 (3) 353 (1998)
https://doi.org/10.1016/S0168-9274(97)00075-5

Bifurcations of finite difference schemes and their approximate inertial forms

Rolf Bronstering and Min Chen
ESAIM: Mathematical Modelling and Numerical Analysis 32 (6) 715 (1998)
https://doi.org/10.1051/m2an/1998320607151

Numerical Methods for Solids (Part 3) Numerical Methods for Fluids (Part 1)

Martine Marion and Roger Temam
Handbook of Numerical Analysis, Numerical Methods for Solids (Part 3) Numerical Methods for Fluids (Part 1) 6 503 (1998)
https://doi.org/10.1016/S1570-8659(98)80010-0

A continuity property for the inverse of mañé's projection

Zdeněk Skalák
Applications of Mathematics 43 (1) 9 (1998)
https://doi.org/10.1023/A:1022291923761

Fifteenth International Conference on Numerical Methods in Fluid Dynamics

Thierry Dubois, Francois Jauberteau and Roger Temam
Lecture Notes in Physics, Fifteenth International Conference on Numerical Methods in Fluid Dynamics 490 388 (1997)
https://doi.org/10.1007/BFb0107133

A parallel spectral Fourier-Nonlinear Galerkin algorithm for simulation of turbulence

A. Averbuch, L. Ioffe, M. Israeli and L. Vozovoi
Numerical Methods for Partial Differential Equations 13 (6) 699 (1997)
https://doi.org/10.1002/(SICI)1098-2426(199711)13:6<699::AID-NUM6>3.0.CO;2-M

Some closure results for inertial manifolds

J. C. Robinson
Journal of Dynamics and Differential Equations 9 (3) 373 (1997)
https://doi.org/10.1007/BF02227487

Arbitrarily accurate approximate inertial manifolds of fixed dimension

James C. Robinson
Physics Letters A 230 (5-6) 301 (1997)
https://doi.org/10.1016/S0375-9601(97)00245-4

Remarks on nonlinear Galerkin method for Kuramoto-Sivashinsky equation

Wu Yujiang
Applied Mathematics and Mechanics 18 (10) 1005 (1997)
https://doi.org/10.1007/BF00189292

Multilevel Methods in Space and Time for the Navier--Stokes Equations

J. B. Burie and M. Marion
SIAM Journal on Numerical Analysis 34 (4) 1574 (1997)
https://doi.org/10.1137/S0036142994267989

The Mathematics of Models for Climatology and Environment

Roger Temam
The Mathematics of Models for Climatology and Environment 181 (1997)
https://doi.org/10.1007/978-3-642-60603-8_5

Dynamical multilevel schemes for the solution of evolution equations by hierarchical finite element discretization

C. Calgaro, J. Laminie and R. Temam
Applied Numerical Mathematics 23 (4) 403 (1997)
https://doi.org/10.1016/S0168-9274(96)00074-8

Stability study, error estimation, and condition number for semi-implicit schemes using incremental unknowns

Francois Pouit
Numerical Methods for Partial Differential Equations 12 (6) 743 (1996)
https://doi.org/10.1002/(SICI)1098-2426(199611)12:6<743::AID-NUM7>3.0.CO;2-S

Modelling of the interaction of lower and higher modes in two-dimensional MHD-equations

Olaf Schmidtmann
Nonlinear Analysis: Theory, Methods & Applications 26 (1) 41 (1996)
https://doi.org/10.1016/0362-546X(94)00207-X

Enslaved finite difference schemes for nonlinear dissipative PDEs

Don A. Jones, Len G. Margolin and Andrew C. Poje
Numerical Methods for Partial Differential Equations 12 (1) 13 (1996)
https://doi.org/10.1002/(SICI)1098-2426(199601)12:1<13::AID-NUM1>3.0.CO;2-Q

Enslaved finite difference approximations for quasigeostrophic shallow flows

Andrew C. Poje, Don A. Jones and Len G. Margolin
Physica D: Nonlinear Phenomena 98 (2-4) 559 (1996)
https://doi.org/10.1016/0167-2789(96)00112-1

Fourier nonlinear Galerkin approximation for the two dimensional Navier-Stokes equations

Hou Yanren
Applied Mathematics and Mechanics 17 (9) 879 (1996)
https://doi.org/10.1007/BF00127187

Alternative approaches to the Karhunen-Loève decomposition for model reduction and data analysis

Michael D. Graham and Ioannis G. Kevrekidis
Computers & Chemical Engineering 20 (5) 495 (1996)
https://doi.org/10.1016/0098-1354(95)00040-2

MULTILEVEL SCHEMES FOR SOLVING UNSTEADY EQUATIONS

O. GOYON
International Journal for Numerical Methods in Fluids 22 (10) 937 (1996)
https://doi.org/10.1002/(SICI)1097-0363(19960530)22:10<937::AID-FLD387>3.0.CO;2-4

Higher-order incremental unknowns, hierarchical basis, and nonlinear dissipative evolutionary equations

Salvador Garcia
Applied Numerical Mathematics 19 (4) 467 (1996)
https://doi.org/10.1016/0168-9274(95)00097-6

The nonlinear galerkin method: A multiscale method applied to the simulation of homogeneous turbulent flows

A. Debussche, T. Dubois and R. Temam
Theoretical and Computational Fluid Dynamics 7 (4) 279 (1995)
https://doi.org/10.1007/BF00312446

Inertial manifolds, partially space-averaged equations, and the separation of scales in turbulent flows*

Oscar Manley, Roger Temam and Shouhong Wang
Physics of Fluids 7 (7) 1791 (1995)
https://doi.org/10.1063/1.868496

Convergence of a chaotic attractor with increased spatial resolution of the Ginzburg-Landau equation

M.S. Jolly, R. Témam and C. Xiong
Chaos, Solitons & Fractals 5 (10) 1833 (1995)
https://doi.org/10.1016/0960-0779(94)00197-X

Finite-dimensional behavior in dissipative partial differential equations

J. C. Robinson
Chaos: An Interdisciplinary Journal of Nonlinear Science 5 (1) 330 (1995)
https://doi.org/10.1063/1.166081

Approximate inertial manifolds of exponential order for semilinear parabolic equations subjected to additive white noise

I. D. Chueshov
Journal of Dynamics and Differential Equations 7 (4) 549 (1995)
https://doi.org/10.1007/BF02218724

On the effectiveness of the approximate inertial manifold?a computational study

Don A. Jones, Len G. Margolin and Edriss S. Titi
Theoretical and Computational Fluid Dynamics 7 (4) 243 (1995)
https://doi.org/10.1007/BF00312444

On computing the long-time solution of the two-dimensional Navier-Stokes equations

M. S. Jolly and C. Xiong
Theoretical and Computational Fluid Dynamics 7 (4) 261 (1995)
https://doi.org/10.1007/BF00312445

Error Estimates on a New Nonlinear Galerkin Method Based on Two-Grid Finite Elements

Martine Marion and Jinchao Xu
SIAM Journal on Numerical Analysis 32 (4) 1170 (1995)
https://doi.org/10.1137/0732054

Full discrete nonlinear galerkin method for the Navier-Stokes equations

Li Kaitai, He Yinnian and Xiang Yimin
Applied Mathematics 9 (1) 11 (1994)
https://doi.org/10.1007/BF02662022

Implementation and numerical analysis of the nonlinear Galerkin methods with finite elements discretization

Jacques Laminie, Frédéric Pascal and Roger Temam
Applied Numerical Mathematics 15 (2) 219 (1994)
https://doi.org/10.1016/0168-9274(94)00021-2

Trends and Perspectives in Applied Mathematics

Roger Temam
Applied Mathematical Sciences, Trends and Perspectives in Applied Mathematics 100 293 (1994)
https://doi.org/10.1007/978-1-4612-0859-4_10

A Remark on Quasi-Stationary Approximate Inertial Manifolds for the Navier–Stokes Equations

D. A. Jones and E. S. Titi
SIAM Journal on Mathematical Analysis 25 (3) 894 (1994)
https://doi.org/10.1137/S0036141092230428

Approximation of exponential order of the attractor of a turbulent flow

A. Debussche and T. Dubois
Physica D: Nonlinear Phenomena 72 (4) 372 (1994)
https://doi.org/10.1016/0167-2789(94)90239-9

Regularity of solutions and approximate inertial manifolds for von Karman evolution equations

I. D. Chueshov
Mathematical Methods in the Applied Sciences 17 (9) 667 (1994)
https://doi.org/10.1002/mma.1670170902

On some dissipative fully discrete nonlinear Galerkin schemes for the Kuramoto-Sivashinsky equation

C. Foias, M.S. Jolly, I.G. Kevrekidis and E.S. Titi
Physics Letters A 186 (1-2) 87 (1994)
https://doi.org/10.1016/0375-9601(94)90926-1

Separation of variables in the Stokes problem application to its finite element multiscale approximation

O. Goubet
ESAIM: Mathematical Modelling and Numerical Analysis 28 (3) 243 (1994)
https://doi.org/10.1051/m2an/1994280302431

Approximation of Attractors by Algebraic or Analytic Sets

C. Foias and R. Temam
SIAM Journal on Mathematical Analysis 25 (5) 1269 (1994)
https://doi.org/10.1137/S0036141091224552

Turbulence in Fluid Flows

George R. Sell
The IMA Volumes in Mathematics and its Applications, Turbulence in Fluid Flows 55 165 (1993)
https://doi.org/10.1007/978-1-4612-4346-5_10

On the Numerical Solution of the Incompressible Navier‐Stokes Equations

R. Rannacher
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 73 (9) 203 (1993)
https://doi.org/10.1002/zamm.19930730903

Nonlinear galerkin methods using hierarchical almost-orthogonal finite elements bases

Olivier Goubet
Nonlinear Analysis: Theory, Methods & Applications 20 (3) 223 (1993)
https://doi.org/10.1016/0362-546X(93)90160-T

Preserving Symmetries in the Proper Orthogonal Decomposition

Nadine Aubry, Wen-Yu Lian and Edriss S. Titi
SIAM Journal on Scientific Computing 14 (2) 483 (1993)
https://doi.org/10.1137/0914030

Implementation of finite element nonlinear Galerkin methods using hierarchical bases

Jacques Laminie, Fr�d�ric Pascal and Roger Temam
Computational Mechanics 11 (5-6) 384 (1993)
https://doi.org/10.1007/BF00350095

Low dimensional approximate inertial manifolds for the kuramoto-sivashinsky equation

Wenhan Chen
Numerical Functional Analysis and Optimization 14 (3-4) 265 (1993)
https://doi.org/10.1080/01630569308816521

Computational efficiency and approximate inertial manifolds for a Bénard convection system

M. D. Graham, P. H. Steen and E. S. Titi
Journal of Nonlinear Science 3 (1) 153 (1993)
https://doi.org/10.1007/BF02429862

Galerkin projections and the proper orthogonal decomposition for equivariant equations

Gal Berkooz and Edriss S. Titi
Physics Letters A 174 (1-2) 94 (1993)
https://doi.org/10.1016/0375-9601(93)90549-F

Bifurcation computations on an approximate inertial manifold for the 2D Navier-Stokes equations

M.S. Jolly
Physica D: Nonlinear Phenomena 63 (1-2) 8 (1993)
https://doi.org/10.1016/0167-2789(93)90143-O

On the rate of convergence of the nonlinear Galerkin methods

Christophe Devulder, Martine Marion and Edriss S. Titi
Mathematics of Computation 60 (202) 495 (1993)
https://doi.org/10.1090/S0025-5718-1993-1160273-1

A convergent family of approximate inertial manifolds

A. Debussche and R. Temam
Applied Mathematics Letters 6 (1) 87 (1993)
https://doi.org/10.1016/0893-9659(93)90155-G

Solution of the incompressible Navier-Stokes equations by the nonlinear Galerkin method

T. Dubois, F. Jauberteau and R. Temam
Journal of Scientific Computing 8 (2) 167 (1993)
https://doi.org/10.1007/BF01060871

Incremental Unknowns in Finite Differences: Condition Number of the Matrix

Min Chen and Roger Temam
SIAM Journal on Matrix Analysis and Applications 14 (2) 432 (1993)
https://doi.org/10.1137/0614031

On the Question of Turbulence Modeling by Approximate Inertial Manifolds and the Nonlinear Galerkin Method

John G. Heywood and Rolf Rannacher
SIAM Journal on Numerical Analysis 30 (6) 1603 (1993)
https://doi.org/10.1137/0730083

A Class of Numerical Algorithms for Large Time Integration: The Nonlinear Galerkin Methods

Christophe Devulder and Martine Marion
SIAM Journal on Numerical Analysis 29 (2) 462 (1992)
https://doi.org/10.1137/0729028

Determining finite volume elements for the 2D Navier-Stokes equations

Don A. Jones and Edriss S. Titi
Physica D: Nonlinear Phenomena 60 (1-4) 165 (1992)
https://doi.org/10.1016/0167-2789(92)90233-D

Approximate inertial manifolds for 2D Navier-Stokes equations

Wenhan Chen
Journal of Mathematical Analysis and Applications 165 (2) 399 (1992)
https://doi.org/10.1016/0022-247X(92)90048-I

On the number of determining nodes for the 2D Navier-Stokes equations

Don A Jones and Edriss S Titi
Journal of Mathematical Analysis and Applications 168 (1) 72 (1992)
https://doi.org/10.1016/0022-247X(92)90190-O

A note on Gevrey class regularity for the solutions of the Navier-Stokes equations

Xiaosong Liu
Journal of Mathematical Analysis and Applications 167 (2) 588 (1992)
https://doi.org/10.1016/0022-247X(92)90226-4

On the construction of families of approximate inertial manifolds

A Debussche and M Marion
Journal of Differential Equations 100 (1) 173 (1992)
https://doi.org/10.1016/0022-0396(92)90131-6

On approximate inertial manifolds for two and three dimensional turbulent flows

Xiaosong Liu
Journal of Mathematical Analysis and Applications 163 (2) 559 (1992)
https://doi.org/10.1016/0022-247X(92)90267-H

Construction of Approximate Inertial Manifolds Using Wavelets

Olivier Goubet
SIAM Journal on Mathematical Analysis 23 (6) 1455 (1992)
https://doi.org/10.1137/0523083

Strongly interacting travelling waves and quasiperiodic dynamics in porous medium convection

Michael D. Graham and Paul H. Steen
Physica D: Nonlinear Phenomena 54 (4) 331 (1992)
https://doi.org/10.1016/0167-2789(92)90042-L

An approximate inertial manifold for computing Burgers' equation

L.G. Margolin and D.A. Jones
Physica D: Nonlinear Phenomena 60 (1-4) 175 (1992)
https://doi.org/10.1016/0167-2789(92)90234-E

Nonlinear galerkin method and subgrid-scale model for two-dimensional turbulent flows

Fr�d�ric Pascal and Claude Basdevant
Theoretical and Computational Fluid Dynamics 3 (5) 267 (1992)
https://doi.org/10.1007/BF00717644

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