Bibliography

Major publications by the team in recent years

1R. 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.
2R. 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.
3R. 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.
4R. 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.
5R. 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/
6D. Braess, R. Hoppe, J. Schoberl.

A A posteriori estimators for obstacle problems by the hypercircle method, in: Comput. Vis. Sci., 2008, vol. 11, n^o 4-6, p. 351-362.
7R. 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.
8D. Papaghiuc, J.-M. Thomas.

Nonconforming finite element methods without numerical locking., in: Numer. Math., 1998, vol. 81, n^o 2, p. 163-186.
9E. 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.
10J.-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

11D. Capatina.

Analyse de méthodes mixtes d'éléments finis en mécanique, Université de Pau et des Pays de l'Adour, November 2011, Habilitation à Diriger des Recherches.

http://hal.inria.fr/tel-00647026/en

Articles in International Peer-Reviewed Journal

12R. Becker, E. Burman, P. Hansbo.

A finite element time relaxation method, in: Comptes Rendus de l Académie des Sciences - Series I - Mathematics, 2011, vol. 349, n^o 5-6, p. 353-356.

http://hal.inria.fr/hal-00645159/en
13R. Becker, E. Burman, P. Hansbo.

A hierarchical NXFEM for fictitious domain simulations, in: International Journal for Numerical Methods in Engineering, 2011, vol. 4-5, p. 549-559.

http://hal.inria.fr/hal-00645157/en
14R. Becker, D. Capatina, D. Graebling, J. Joie.

Nonconforming finite element approximation of the Giesekus model for polymer flows, in: Computers and Fluids, 2011, vol. 46, p. 142 - 147.

http://hal.inria.fr/hal-00645152/en
15R. Becker, D. Capatina, J. Joie.

Connections between discontinuous Galerkin and nonconforming finite element methods for the Stokes equations, in: Numerical Methods for Partial Differential Equations / Numerical Methods for Partial Differential Equations An International Journal, March 2011, n^o DOI: 10.1002/num.20671. [ DOI : 10.1002/num.20671 ]

http://hal.inria.fr/inria-00537872/en
16R. Becker, S. Mao.

Quasi-optimality of adaptive non-conforming finite element methods for the Stokes equations, in: SIAM Journal on Numerical Analysis, 2011, vol. 49, n^o 3, p. 970-991.

http://hal.inria.fr/hal-00645150/en
17R. Becker, D. Trujillo.

A remark on the optimality of adaptive finite element methods, in: Comptes Rendus de l Académie des Sciences - Series I - Mathematics, 2011, vol. 349, p. 225-228.

http://hal.inria.fr/hal-00645158/en
18R. Becker, D. Trujillo.

Concepts of the finite element library Concha, in: Monografias Matematicas Garcia de Galdeano, December 2011, vol. 35, p. 59-67.

http://hal.inria.fr/hal-00649001/en
19R. Becker, D. Trujillo, E. Estecahandy.

Weighted marking for goal-oriented adaptive finite element methods, in: SIAM Journal on Numerical Analysis, 2011.

http://hal.inria.fr/hal-00647356/en
20D. Capatina, N. Barrau.

Numerical simulation of anisothermal flows of Newtonian fluids, in: Monografias Matematicas Garcia de Galdeano, 2011, vol. 35, p. 37-46.

http://hal.inria.fr/hal-00646561/en
21M. Li, R. Becker, S. Mao.

A remark on supercloseness and extrapolation of the quadrilateral han element for the stokes equations, in: Comptes Rendus de l Académie des Sciences - Series I - Mathematics, 2011, vol. 349, n^o 17-18, p. 1017 - 1020.

http://hal.inria.fr/hal-00645148/en
22C. Xiong, Y. Li.

A posteriori error estimators for optimal distributed control governed by the first-order linear hyperbolic equation: DG method, in: Numerical Methods for Partial Differential Equations, 2011, vol. 27, n^o 3, p. 491-506.

http://hal.inria.fr/hal-00646952/en
23C. Xiong, Y. Li.

Error analysis for optimal control problem governed by convection diffusion equations: DG method, in: Journal of Computational and Applied Mathematics, 2011, vol. 235, n^o 10, p. 3163-3177.

http://hal.inria.fr/hal-00646954/en

Invited Conferences

24D. Capatina.

A positivity preserving discontinuous Galerkin method with applications in polymer flows, in: Int. Conf. " Mathematical Fluid Mechanics and Biomedical Applications", Ponta Delgada, Portugal, November 2011.

http://hal.inria.fr/hal-00646529/en
25D. Capatina.

Numerical analysis of a Riccati type matrix transport equation, in: 7th Workshop "Variational Multiscale Methods", Glasgow, United Kingdom, November 2011.

http://hal.inria.fr/hal-00646527/en

International Conferences with Proceedings

26R. Becker, D. Capatina, R. Luce.

A posteriori error estimators based on H(div)- reconstruction for diffusion-convection-reaction equation, in: 9th Enumath, Leicester, United Kingdom, November 2011.

http://hal.inria.fr/hal-00646537/en
27R. Becker, K. Gokpi, É. Schall, D. Trujillo.

A posteriori error estimators for grid adaptation with Galerkin discontinuous finite element method, in: 8th Int. Conf. on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT), Pointe Aux Piments, Mauritius, November 2011.

http://hal.inria.fr/hal-00646856/en
28R. Becker, K. Gokpi, É. Schall, D. Trujillo.

Comparison of two types of a posteriori error estimators on mesh adaptation in discontinuous Galerkin finite elements methods, in: 4th European Conference for Aerospace Sciences (EUCASS), St. Petersburg, Russian Federation, November 2011.

http://hal.inria.fr/hal-00646853/en

Conferences without Proceedings

29R. Becker.

Adaptive Finite Element Methods for incompressible flow problems, in: 16th Int. Conf. on Finite Elements for Flow Problems, München, Germany, November 2011.

http://hal.inria.fr/hal-00646745/en
30R. Becker.

Adaptive Finite Elements for sensitivity computations, in: Workshop on Discretization methods for fluid flows, Marseille, France, September 2011.

http://hal.inria.fr/hal-00646746/en
31R. Becker, D. Capatina.

Numerical analysis of a matrix-valued transport equation with applications in non-Newtonian flows, in: 7th ICIAM, Vancouver, Canada, November 2011.

http://hal.inria.fr/hal-00646530/en
32R. Becker, D. Capatina, D. Graebling, J. Joie.

Robust approximation of Giesekus flow by nonconforming finite elements, in: 16th Int. Conf. on Finite Elements for Flow Problems, Münich, Germany, November 2011.

http://hal.inria.fr/hal-00646535/en
33R. Becker, D. Capatina, R. Luce, D. Trujillo.

A posteriori error estimation for sensitivity analysis in finite element methods, in: 11th US National Congress on Computational Mechanics, Minneapolis, United States, November 2011.

http://hal.inria.fr/hal-00646533/en

Other Publications

34C. Amrouche, N. E. H. Seloula.

Lp-Theory for Vector Potentials and Sobolev's Inequalities for Vector Fields, 2011, 7 pages.

http://hal.inria.fr/hal-00629127/en
35C. Amrouche, N. E. H. Seloula.

Stokes Equations and Elliptic Systems With Non Standard Boundary Conditions, 2011, 8 pages.

http://hal.inria.fr/hal-00629131/en

References in notes

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37G. Baker.

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38N. Barrau, D. Capatina.

Numerical simulation of anisothermal flows of Newtonian fluids, in: 11th International Conference Zaragoza-Pau on Applied Mathematics and Statistics, Espagne Jaca, 2010.

http://hal.inria.fr/inria-00539640/en
39F. Bassi, S. Rebay.

High-order accurate discontinuous finite element solution of the 2D Euler equations, in: J. Comput. Phys., 1997, vol. 138, n^o 2, p. 251–285.
40R. 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/
41R. Becker, E. Burman, P. Hansbo.

A hierarchical nxfem for fictitious domain simulations, in: Int. J. Numer. Meth. Engng, 2010, to appear.

http://hal.inria.fr/inria-00539171/en
42R. 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/
43R. Becker, P. Hansbo.

A simple pressure stabilization method for the Stokes equation, in: Comm. Numer. Methods Eng., 2008, vol. 24, n^o 11, p. 1421-1430.
44R. Becker, C. Johnson, R. Rannacher.

Adaptive Error Control for Multigrid Finite Element Methods, in: Computing, 1995, vol. 55, p. 271-288.
45R. Becker, S. Mao.

An optimally convergent adaptive mixed finite element method, in: Numer. Math., 2008, vol. 111, n^o 1, p. 35-54.
46R. Becker, S. Mao.

Convergence and quasi-optimal complexity of a simple adaptive finite element method, in: M2AN, 2009, vol. 43, p. 1203–1219.

http://dx.doi.org/10.1051/m2an/2009036
47R. Becker, R. Rannacher.

An optimal control approach to a posteriori error estimation in finite element methods, in: Acta Numer., 2001, vol. 10, p. 1–102.

http://dx.doi.org/10.1017/S0962492901000010
48R. Becker, R. Rannacher.

Weighted a posteriori error control in FE methods, in: ENUMATH'97, H. G. Bock, et al. (editors), World Sci. Publ., Singapore, 1995.
49R. Becker, S. Mao, Z. Shi.

A convergent nonconforming adaptive finite element method with optimal complexity, in: SIAM Journal on Numerical Analysis, 2010, vol. 47, p. 4639–4659.

http://hal.inria.fr/inria-00438541/en/
50P. Binev, W. Dahmen, R. DeVore.

Adaptive finite element methods with convergence rates., in: Numer. Math., 2004, vol. 97, n^o 2, p. 219-268.
51S. Boyaval, T. Lelièvre, C. Mangoubi.

Free-energy-dissipative schemes for the Oldroyd-B model, INRIA, 2008, n^o RR-6413.
52M. Braack, E. Burman.

Local Projection Stabilization for the Oseen Problem and its Interpretation as a Variational Multiscale Method, in: SIAM J. Numer. Anal., 2006, vol. 43, n^o 6, p. 2544-2566.
53D. Braess, R. Hoppe, J. Schoberl.

A A posteriori estimators for obstacle problems by the hypercircle method, in: Comput. Vis. Sci., 2008, vol. 11, n^o 4-6, p. 351-362.
54A. Brooks, T. Hughes.

Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations., in: Comput. Methods Appl. Mech. Comput. Methods Appl. Mech. Engrg., 1982, vol. 32, p. 199-259.
55E. Burman, M. A. Fernández.

Galerkin finite element methods with symmetric pressure stabilization for the transient Stokes equations: stability and convergence analysis, in: SIAM J. Numer. Anal., 2008, vol. 47, n^o 1, p. 409–439.

http://dx.doi.org/10.1137/070707403
56E. Burman, P. Hansbo.

Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems., in: Comput. Methods Appl. Mech. Engrg., 2004, vol. 193, n^o 15-16, p. 1437-1453.
57H. Damanik, J. Hron, A. Ouazzi, S. Turek.

A monolithic FEM approach for the log-conformation reformulation (LCR) of viscoelastic flow problems, in: Journal of Non-Newtonian Fluid Mechanics, 2010, vol. 165, 1105 p.
58H.-S. Dou, N. Phan-Thien.

The flow of an Oldroyd-B fluid past a cylinder in a channel: adaptive viscosity vorticity (DAVSS- $ω$ ) formulation, in: Journal of Non-Newtonian Fluid Mechanics, 1999, vol. 87, 47 p.
59E. 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/
60E. 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/
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Stabilization of Galerkin approximations of transport equations by subgrid modeling, in: Modél. Math. Anal. Numér., 1999, vol. 33, n^o 6, p. 1293-1316.
62A. 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.
63A. 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.
64D. Hu, T. Lelièvre.

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