Overall Objectives
Scientific Foundations
Application Domains
New Results
Contracts and Grants with Industry
Other Grants and Activities


Major publications by the team in recent years

R. Becker, M. Braack.
A Finite Element Pressure Gradient Stabilization for the Stokes Equations Based on Local Projections, in: Calcolo, 2001, vol. 38, no 4, p. 173–199.
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.
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.
R. Becker, B. Vexler.
Mesh Refinement and Numerical Sensitivity Analysis for Parameter Calibration of Partial Differential Equations, in: J. Comput. Phys., 2005, vol. 206, no 1, p. 95-110.
R. Becker, S. Mao, Z.-C. Shi.
A convergent adaptive finite element method with optimal complexity, in: Electronic Transactions on Numerical Analysis, 2008
D. Capatina-Papaghiuc, J.-M. Thomas.
Nonconforming finite element methods without numerical locking., in: Numer. Math., 1998, vol. 81, no 2, p. 163-186.
R. Luce, B. Wohlmuth.
A local a posteriori error estimator based on equilibrated fluxes., in: SIAM J. Numer. Anal., 2004, vol. 42, no 4, p. 1394-1414.
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, no 20, p. 3909-3926.
J.-M. Thomas, D. Trujillo.
Mixed finite volume methods., in: Int. J. Numer. Methods Engrg., 1999, vol. 46, no 9, p. 1351-1366.

Publications of the year

Doctoral Dissertations and Habilitation Theses

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

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, no 41-44, p. 3352-3360
R. Becker, S. Mao.
Convergence and quasi-optimal complexity of a simple adaptive finite element method, in: M2AN, 2009, vol. 43, p. 1203–1219
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, no 2, p. 1470-1499
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, no 10-11, p. 1509-1525
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
E. Dubach, R. Luce, J. Thomas.
Pseudo-conforming polynomial finite element on quadrilaterals, in: Int. J. Comput. Math., 2009, vol. 80, no 10-11, p. 1798-1816

Invited Conferences

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
D. Capatina.
Finite element approximation of polymer flows preserving positivity, in: Computational Multiscale Methods, Enschede (The Netherlands), 2009

International Peer-Reviewed Conference/Proceedings

M. Amara, A. Petrau, D. Trujillo.
Finite Element Approximation of a Quasi-3D Model for the River Flow, in: ENUMATH 2009, Suède Uppsala, 2009
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
R. Becker, D. Capatina.
Finite element approximation of Giesekus model for polymer flows, in: Enumath, Suède Uppsala, 2009
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
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
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
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
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
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
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

Workshops without Proceedings

R. Becker.
Adaptive finite elements for the Stokes equations, in: Numerical analysis seminar, Allemagne Dortmund, 2009
R. Becker, D. Capatina.
A DG method for the Stokes equations related to nonconforming finite element methods, in: Mafelap, Royaume-Uni Londres, 2009
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
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
D. Trujillo, M. Amara, A. Petrau.
Coupling of Models for the Quasi-3D Hydrodynamical Modeling, in: Coupled Problems 2009, Italie Ischia, 2009

Internal Reports

R. Becker, D. Capatina, J. Joie.
A dG method for the Stokes equations related to nonconforming approximations, INRIA, 2009, Rapport de recherche.

Other Publications

C. Amrouche, F. Dahoumane, R. Luce, G. Vallet.
On the hydrostatic Stokes approximation with non homogeneous boundary conditions, 2009
R. Becker, S. Mao, Z. Shi.
A convergent nonconforming adaptive finite element method with quasi-optimal complexity, 2009, to appear in SINUM.

References in notes

J. D. Buckmaster (editor)
The mathematics of combustion, SIAM - Society for Industrial and Applied Mathematics., 1985.
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.
D. Arnold, D. Boffi, R. Falk.
Approximation by quadrilateral finite elements., in: Math. Comp., 2002, vol. 71, no 239, p. 909-922.
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.
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, no 5, p. 813-833.
R. Becker, B. Vexler.
A posteriori error estimation for finite element discretizations of parameter identification problems, in: Numer. Math., 2004, vol. 96, no 3, p. 435–459.
R. Becker, S. Mao.
An optimally convergent adaptive mixed finite element method, in: Numerische Mathematik, 2008, vol. 111, p. 35-54
R. Becker, D. Trujillo.
Convergence of an adaptive finite element method on quadrilateral meshes, INRIA, 2008, no RR-6740, Research Report.
P. Binev, W. Dahmen, R. DeVore.
Adaptive finite element methods with convergence rates., in: Numer. Math., 2004, vol. 97, no 2, p. 219-268.
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Free-energy-dissipative schemes for the Oldroyd-B model, INRIA, 2008, no RR-6413, Technical report.
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A posteriori control of modeling errors and discretization errors., in: Multiscale Model. Simul., 2003, vol. 1, no 2, p. 221-238.
M. Braack, A. Ern.
Coupling multimodelling with local mesh refinement for the numerical computation of laminar flames., in: Combust. Theory Model., 2004, vol. 8, no 4, p. 771-788.
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Discontinuous Galerkin methods for first-order hyperbolic problems., in: Math. Models Methods Appl. Sci., 2004, vol. 14, no 12, p. 1893-1903.
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A unified analysis for conforming and nonconforming stabilized finite element methods using interior penalty., in: SIAM J. Numer. Anal., 2005, vol. 43, no 5, p. 2012-2033.
E. Burman, B. Stamm.
Discontinuous and Continuous Finite Element Methods with Interior Penalty for Hyperbolic Problems, in: J. Numer. Math.,, 2005.
R. Fattal, R. Kupferman.
Constitutive laws for the matrix-logarithm of the conformation tensor, in: Journal of Non-Newtonian Fluid Mechanics, 2004, vol. 123, no 2-3, p. 281–285.
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, no 47-48, p. 537-5552.
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A finite element method for the simulation of strong and weak discontinuities in solid mechanics., in: Comput. Methods Appl. Mech. Eng., 2004, vol. 193, no 33-35, p. 3523-3540.
R. Hartmann, P. Houston, E. Süli.
hp-Discontinuous Galerkin finite element methods for problems: error analysis and adaptivity, Oxford University, Computation Laboratory, 2001, no NA-01/07, Research Report.
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New entropy estimates for Oldroyd-B and related models, in: Commun. Math. Sci., 2007, vol. 5, no 4, p. 909–916.
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Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge University Press, Cambridge-Lund, 1987.
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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.
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New formulations, positivity preserving discretizations and stability analysis for non-Newtonian flow models, Pennstate, 2004, Technical report.
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Data oscillation and convergence of adaptive FEM., in: SIAM J. Numer. Anal., 2000, vol. 38, no 2, p. 466-488.
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Estimation of modeling error in computational mechanics., in: J. Comput. Phys., 2002, vol. 182, no 2, p. 496-515.
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Computational Rheology, Imperial College Press, London, 2002.
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Theoretical and Numerical Combustion, Edwards Philadelphia, 2001.
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Intrinsic low-dimensional manifolds of strained and unstrained flames., in: Combust. Theory Model., 1998, vol. 2, no 2, p. 135-152.
R. Stevenson.
Optimality of a standard adaptive finite element method, in: Found. Comput. Math., 2007, vol. 7, no 2, p. 245-269.
R. Verfürth.
A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley/Teubner, New York-Stuttgart, 1996.
J. Warnatz, U. Maas, R. Dibble.
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