Bibliography

Major publications by the team in recent years

[1]

R. Becker, M. Braack.
A Finite Element Pressure Gradient Stabilization for the Stokes Equations Based on Local Projections, in: Calcolo, 2001, vol. 38, n^o 4, p. 173–199.

[2]

R. Becker, R. Rannacher.
An Optimal Control Approach to A-Posteriori Error Estimation, in: Acta Numerica 2001, A. Iserles (editor), Cambridege University Press, 2001, p. 1–102.

[3]

R. Becker, R. Rannacher.
A feed-back approach to error control in finite element methods: Basic analysis and examples, in: East-West J. Numer. Math., 1996, vol. 4, p. 237–264.

[4]

R. Becker, B. Vexler.
Mesh Refinement and Numerical Sensitivity Analysis for Parameter Calibration of Partial Differential Equations, in: J. Comput. Phys., 2005, vol. 206, n^o 1, p. 95-110.

[5]

R. Becker, S. Mao, Z.-C. Shi.
A convergent adaptive finite element method with optimal complexity, in: Electronic Transactions on Numerical Analysis, 2008
http://hal.inria.fr/inria-00343020/en/.

[6]

D. Capatina-Papaghiuc, J.-M. Thomas.
Nonconforming finite element methods without numerical locking., in: Numer. Math., 1998, vol. 81, n^o 2, p. 163-186.

[7]

R. Luce, B. Wohlmuth.
A local a posteriori error estimator based on equilibrated fluxes., in: SIAM J. Numer. Anal., 2004, vol. 42, n^o 4, p. 1394-1414.

[8]

E. Schall, C. Viozat, B. Koobus, A. Dervieux.
Computation of low Mach thermical flows with implicit upwind methods., in: Int. J. Heat Mass Transfer, 2003, vol. 46, n^o 20, p. 3909-3926.

[9]

J.-M. Thomas, D. Trujillo.
Mixed finite volume methods., in: Int. J. Numer. Methods Engrg., 1999, vol. 46, n^o 9, p. 1351-1366.

Publications of the year

Doctoral Dissertations and Habilitation Theses

[10]

R. Luce.
Modélisations et Simulations numériques. Eléments finis Pseudo-conformes pour quadrilatères et hexaèdres, LMAP, Université de Pau, 2009, Habilitation à Diriger des Recherches.

Articles in International Peer-Reviewed Journal

[11]

R. Becker, E. Burman, P. Hansbo.
A Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity, in: Comput. Methods Appl. Mech. Engrg., 2009, vol. 198, n^o 41-44, p. 3352-3360
http://hal.inria.fr/inria-00437190/en/.

[12]

R. Becker, S. Mao.
Convergence and quasi-optimal complexity of a simple adaptive finite element method, in: M2AN, 2009, vol. 43, p. 1203–1219
http://hal.inria.fr/inria-00437458/en/.

[13]

D. Capatina, M. Amara, L. Lizaik.
Coupling of Darcy-Forchheimer and compressible Navier-Stokes equations with heat transfer, in: SIAM J. Sci. Comp., 2009, vol. 31, n^o 2, p. 1470-1499
http://hal.inria.fr/inria-00437566/en/.

[14]

D. Capatina, L. Lizaik, P. Terpollili.
Numerical modeling of multi-component multi-phase flows in petroleum reservoirs with heat transfer, in: Appl. Analysis, 2009, vol. 88, n^o 10-11, p. 1509-1525
http://hal.inria.fr/inria-00437571/en/.

[15]

E. Dubach, R. Luce, J. Thomas.
Pseudo-conform polynomial Lagrange finite elements on quadrilaterals and hexahedra., in: Comm. Pure Appl. Anal., 2009, vol. 8, p. 237-254
http://hal.inria.fr/inria-00438537/en/.

[16]

E. Dubach, R. Luce, J. Thomas.
Pseudo-conforming polynomial finite element on quadrilaterals, in: Int. J. Comput. Math., 2009, vol. 80, n^o 10-11, p. 1798-1816
http://hal.inria.fr/inria-00438536/en/.

Invited Conferences

[17]

R. Becker.
Convergence and quasi-optimality of adaptive finite element methods for the Stokes equations, in: XXI Cedya 2009, Espagne Ciudad Real, Departament of Mathematics and the Institute of Applied Mathematics in Science and Engineering at University of Castilla - La Mancha, 2009
http://hal.inria.fr/inria-00437853/en/.

[18]

D. Capatina.
Finite element approximation of polymer flows preserving positivity, in: Computational Multiscale Methods, Enschede (The Netherlands), 2009
http://hal.inria.fr/inria-00437560/en/.

International Peer-Reviewed Conference/Proceedings

[19]

M. Amara, A. Petrau, D. Trujillo.
Finite Element Approximation of a Quasi-3D Model for the River Flow, in: ENUMATH 2009, Suède Uppsala, 2009
http://hal.inria.fr/inria-00438221/en/.

[20]

M. Amara, Y. Moguen, E. Schall.
Asymptotic kinetic energy conservation for low-mach number flow computations, in: Tenth International Conference Zaragoza-Pau on Applied Mathematics and Statistics, Jaca Espagne, 2009
http://hal.inria.fr/inria-00438989/en/.

[21]

R. Becker, D. Capatina.
Finite element approximation of Giesekus model for polymer flows, in: Enumath, Suède Uppsala, 2009
http://hal.inria.fr/inria-00437561/en/.

[22]

R. Becker, D. Capatina, D. Graebling, j. Joie.
Nonconforming finite element discretization for the numerical simulation of polymer flows, in: Tenth International Conference Zaragoza-Pau on Applied Mathematics and Statistics, Espagne Jaca, 2009
http://hal.inria.fr/inria-00438546/en/.

[23]

R. Becker, D. Capatina, j. Joie.
A new DG method for the Stokes problem wit a priori and a posteriori error analysis, in: ENUMATH, Suède Uppsala, 2009
http://hal.inria.fr/inria-00437565/en/.

[24]

R. Becker, N. E. H. Seloula.
Numerical simulation of liquid crystals, in: Tenth International Conference Zaragoza-Pau on Applied Mathematics and Statistics, Espagne Jaca, 2009
http://hal.inria.fr/inria-00438545/en/.

[25]

R. Becker, D. Capatina, J. Joie.
A new DG method for the Stokes problem with a priori and a posteriori error analysis, in: Mamern 09, Pau France, 2009
http://hal.inria.fr/inria-00438988/en/.

[26]

R. Luce, C. Poutous, J. Thomas.
Condition affaiblies d'admissibilité pour une densité surfacique de force dans les problème de coques en membranes inhibées, in: Colloque franco-roumain de mathématiques appliquées, Roumanie Brasov, 2009
http://hal.inria.fr/inria-00438539/en/.

[27]

R. Luce, J. Thomas.
Pseudo-Conforming Finite Elements H 1 and H(div ) Approximations on Hexahedral Meshes, in: Current and New Trends in Scientific Computing CMM, Chili Santiago de Chile, 2009
http://hal.inria.fr/inria-00438540/en/.

[28]

V. Perrier.
Simulation of phase transition in a compressible isothermal fluid governed by the van-der-Waals equation of state, in: Numerical approximations of hyperbolic systems with source terms and applications, Castro-Urdiales Espagne, 2009
http://hal.inria.fr/inria-00440466/en/.

Workshops without Proceedings

[29]

R. Becker.
Adaptive finite elements for the Stokes equations, in: Numerical analysis seminar, Allemagne Dortmund, 2009
http://hal.inria.fr/inria-00437856/en/.

[30]

R. Becker, D. Capatina.
A DG method for the Stokes equations related to nonconforming finite element methods, in: Mafelap, Royaume-Uni Londres, 2009
http://hal.inria.fr/inria-00437563/en/.

[31]

R. Becker, N. E. H. Seloula.
A discontinous Galerkin Method for the Navier-Stokes Equations with Different Boundary Conditions, in: MAMERN 09, France Pau, 2009
http://hal.inria.fr/inria-00438542/en/.

[32]

D. Capatina, L. Lizaik, P. Terpollili.
Finite Volume Approximation of a Multi-Component Multi-Phase Reservoir Model with Heat Transfer, in: SIAM Geosciences, Allemagne Leipzig, 2009
http://hal.inria.fr/inria-00437564/en/.

[33]

D. Trujillo, M. Amara, A. Petrau.
Coupling of Models for the Quasi-3D Hydrodynamical Modeling, in: Coupled Problems 2009, Italie Ischia, 2009
http://hal.inria.fr/inria-00438220/en/.

Internal Reports

[34]

R. Becker, D. Capatina, J. Joie.
A dG method for the Stokes equations related to nonconforming approximations, INRIA, 2009
http://hal.inria.fr/inria-00380772/en/, Rapport de recherche.

Other Publications

[35]

C. Amrouche, F. Dahoumane, R. Luce, G. Vallet.
On the hydrostatic Stokes approximation with non homogeneous boundary conditions, 2009
http://hal.inria.fr/inria-00438538/en/.

[36]

R. Becker, S. Mao, Z. Shi.
A convergent nonconforming adaptive finite element method with quasi-optimal complexity, 2009
http://hal.inria.fr/inria-00438541/en/, to appear in SINUM.

References in notes

[37]

J. D. Buckmaster (editor)
The mathematics of combustion, SIAM - Society for Industrial and Applied Mathematics., 1985.

[38]

M. Amara, D. Capatina-Papaghiuc, D. Trujillo.
Variational approach for the multiscale modeling of a river flow. Part 1 : Derivation of hydrodynamical models, LMA, UPPA, 2006, Technical report.

[39]

D. Arnold, D. Boffi, R. Falk.
Approximation by quadrilateral finite elements., in: Math. Comp., 2002, vol. 71, n^o 239, p. 909-922.

[40]

R. Becker, M. Braack, R. Rannacher.
Numerical simulation of laminar flames at low Mach number with adaptive finite elements, in: Combust. Theory Model., 1999, vol. 3, p. 503–534.

[41]

R. Becker, D. Meidner, B. Vexler.
Efficient numerical solution of parabolic optimization problems by finite element methods, in: Optimization Methods and Software, 2007, vol. 22, n^o 5, p. 813-833.

[42]

R. Becker, B. Vexler.
A posteriori error estimation for finite element discretizations of parameter identification problems, in: Numer. Math., 2004, vol. 96, n^o 3, p. 435–459.

[43]

R. Becker, S. Mao.
An optimally convergent adaptive mixed finite element method, in: Numerische Mathematik, 2008, vol. 111, p. 35-54
http://hal.inria.fr/inria-00343018/en/.

[44]

R. Becker, D. Trujillo.
Convergence of an adaptive finite element method on quadrilateral meshes, INRIA, 2008, n^o RR-6740
http://hal.inria.fr/inria-00342672/en/, Research Report.

[45]

P. Binev, W. Dahmen, R. DeVore.
Adaptive finite element methods with convergence rates., in: Numer. Math., 2004, vol. 97, n^o 2, p. 219-268.

[46]

S. Boyaval, T. Lelièvre, C. Mangoubi.
Free-energy-dissipative schemes for the Oldroyd-B model, INRIA, 2008, n^o RR-6413, Technical report.

[47]

M. Braack, A. Ern.
A posteriori control of modeling errors and discretization errors., in: Multiscale Model. Simul., 2003, vol. 1, n^o 2, p. 221-238.

[48]

M. Braack, A. Ern.
Coupling multimodelling with local mesh refinement for the numerical computation of laminar flames., in: Combust. Theory Model., 2004, vol. 8, n^o 4, p. 771-788.

[49]

F. Brezzi, L. Marini, E. Süli.
Discontinuous Galerkin methods for first-order hyperbolic problems., in: Math. Models Methods Appl. Sci., 2004, vol. 14, n^o 12, p. 1893-1903.

[50]

E. Burman.
A unified analysis for conforming and nonconforming stabilized finite element methods using interior penalty., in: SIAM J. Numer. Anal., 2005, vol. 43, n^o 5, p. 2012-2033.

[51]

E. Burman, B. Stamm.
Discontinuous and Continuous Finite Element Methods with Interior Penalty for Hyperbolic Problems, in: J. Numer. Math.,, 2005.

[52]

R. Fattal, R. Kupferman.
Constitutive laws for the matrix-logarithm of the conformation tensor, in: Journal of Non-Newtonian Fluid Mechanics, 2004, vol. 123, n^o 2-3, p. 281–285.

[53]

A. Hansbo, P. Hansbo.
An unfitted finite element method, based on Nitsche's method, for elliptic interface problems, in: Comp. Methods Appl. Mech. Engrg. in Applied Mechanics and Engineering, 2002, vol. 191, n^o 47-48, p. 537-5552.

[54]

A. Hansbo, P. Hansbo.
A finite element method for the simulation of strong and weak discontinuities in solid mechanics., in: Comput. Methods Appl. Mech. Eng., 2004, vol. 193, n^o 33-35, p. 3523-3540.

[55]

R. Hartmann, P. Houston, E. Süli.
hp-Discontinuous Galerkin finite element methods for problems: error analysis and adaptivity, Oxford University, Computation Laboratory, 2001, n^o NA-01/07, Research Report.

[56]

D. Hu, T. Lelièvre.
New entropy estimates for Oldroyd-B and related models, in: Commun. Math. Sci., 2007, vol. 5, n^o 4, p. 909–916.

[57]

C. Johnson.
Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge University Press, Cambridge-Lund, 1987.

[58]

B. Larrouturou, B. Sportisse.
Some mathematical and numerical aspects of reduction in chemical kinetics., in: Computational science for the 21st century. Dedicated to Prof. Roland Glowinski on the occasion of his 60th birthday. Symposium, Tours, France, May 5–7, 1997. Chichester: John Wiley & Sons. 422-431 , Bristeau, M.-O. et al., 1997.

[59]

Y.-J. Lee, J. Xu.
New formulations, positivity preserving discretizations and stability analysis for non-Newtonian flow models, Pennstate, 2004, Technical report.

[60]

P. Morin, R. H. Nochetto, K. G. Siebert.
Data oscillation and convergence of adaptive FEM., in: SIAM J. Numer. Anal., 2000, vol. 38, n^o 2, p. 466-488.

[61]

J. Oden, S. Prudhomme.
Estimation of modeling error in computational mechanics., in: J. Comput. Phys., 2002, vol. 182, n^o 2, p. 496-515.

[62]

R. G. Owens, T. N. Phillips.
Computational Rheology, Imperial College Press, London, 2002.

[63]

T. Poinsot, D. Veynante.
Theoretical and Numerical Combustion, Edwards Philadelphia, 2001.

[64]

D. Schmidt, T. Blasenbrey, U. Maas.
Intrinsic low-dimensional manifolds of strained and unstrained flames., in: Combust. Theory Model., 1998, vol. 2, n^o 2, p. 135-152.

[65]

R. Stevenson.
Optimality of a standard adaptive finite element method, in: Found. Comput. Math., 2007, vol. 7, n^o 2, p. 245-269.

[66]

R. Verfürth.
A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley/Teubner, New York-Stuttgart, 1996.

[67]

J. Warnatz, U. Maas, R. Dibble.
Combustion. Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation, Berlin: Springer, 2001.

[68]

F. Williams.
Combustion Theory, Benjamin Cummins, 1985.