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Laboratoire de mathématiques et de leurs applications (LMAP)
Vous êtes ici :

Roland BeckerProfesseur

  • Equipe "Méthodes Numériques et Fluides Complexes"
  • Parcours
  • Thèmes de recherche
  • Publications

Parcours

  • Head of the INRIA project Concha 2007-2013
  • Doctoral thesis, University of Heidelberg 1996
  • DEA d'Analyse numérique, University of Paris 6 1991

Thèmes de recherche

  • Review of some Mathematics
  • Python
  • NumPy and SciPy
  • Numerical linear algebra

Publications

  • R. Becker, D. Capatina, and R. Luce. Local Flux Reconstructions for Standard Finite Element Methods on Triangular Meshes. SIAM J. Numer. Anal., 54(4):2684–2706, (2016).
  • R. Becker, D. Capatina, R. Luce, and D. Trujillo. Finite element formulation of general boundary conditions for incompressible flows. Comput. Methods Appl. Mech. Eng., 295:240–267, (2015).
  • R. Becker, D. Capatina, R. Luce, and D. Trujillo. Stabilized finite element formulation with domain decomposition for incompressible flows. SIAM J. Sci. Comput., 37(3):1270–1296, (2015).
  • M. Bittl, D. Kuzmin, and R. Becker. The CG1-DG2 method for convection-diffusion equations in 2D. J. Comput. Appl. Math. 270(21-31), (2014).
  • N. Barrau, R. Becker, E. Dubach, and R.Luce. A robust variant of NXFEM for the interface problem. C. R. Math. Acad. Sci. Paris, 350(15):789–792, (2012).
  • R. Becker, D. Capatina, and J. Joie, Connections between discontinuous Galerkin and nonconforming finite element methods for the Stokes equations, Numer. Meth. Part. Diff. Equ., 28(3):1013-1041 (2012).
  • R. Becker, K. Gokpi, E. Schall and D. Trujillo: Fully implicit adaptive method using discontinuous Galerkin finite elements for high speed flows, Int. J. Aerodynamics, 2, (2012).
  • R. Becker, K. Gokpi, E. Schall and D. Trujillo: Comparison of hierarchical and non-hierarchical error indicators for adaptive mesh refinement for the Euler equations, J. Aerospace Eng. (2012).
  • M. Li, R. Becker, and S. Mao. A remark on supercloseness and extrapolation of the quadrilateral Han element for the Stokes equations. Comptes Rendus Mathematique, 349(17-18):1017–1020, (2011).
  • R. Becker, E. Estecahandy, and D. Trujillo. Weighted marking for goal-oriented adaptive finite element methods. SIAM J Numer. Anal., 49(6):2451–2469, (2011).

  • R. Becker and S. Mao. Quasi-optimality of adaptive non-conforming finite element methods for the Stokes equations. SIAM J Numer. Anal., 49(3):970–991, (2011).
  • R. Becker, D. Capatina, D. Graebling, and J. Joie, Nonconforming finite element approximation of the Giesekus model for polymer flows, Computers & Fluids, 46 (2011), pp. 142 – 147.
  • R. Becker, E. Burman, and P. Hansbo, A hierarchical NXFEM for fictitious domain simulations, Internat. J. Numer. Methods Engrg. 86/4-5 (2011) 549-559.
  • R. Becker and D. Trujillo, A remark on the optimality of adaptive finite element methods, C. R. Math. Acad. Sci. Paris, 349 (2011), pp. 225–228.
  • R. Becker, E. Burman, and P. Hansbo. A finite element time relaxation method. C. R. Acad. Sci. Paris, 349(5-6):353–356, (2011).
  • R. Becker, S. Mao, and D. Trujillo. Adaptive nonconforming finite elements for the Stokes equations. Bol. Soc. Esp. Mat. Apl. S⃗eMA, vol. 50, pp.99–113 (2010).
  • R. Becker, S. Mao, and Z.-C. Shi, A convergent nonconforming adaptive finite element method with optimal complexity, SIAM J Numer. Anal., vol. 47, no. 6, pp. 4639–4659, (2010).
  • R. Becker and S. Mao, Convergence and quasi-optimal complexity of a simple adaptive finite element method, M2AN, vol. 43, pp. 1203–1219 (2009).
  • R. Becker, E. Burman, and P. Hansbo, A Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity, Comput. Methods Appl. Mech. Engrg., vol. 198, no. 41-44, pp. 3352–3360 (2009).
  • R. Becker and S. Mao, An optimally convergent adaptive mixed finite element method, Numer. Math., vol. 111, no. 1, pp. 35–54 (2008).
  • R. Becker, S. Mao, and Z.-C. Shi, A convergent adaptive finite element method with optimal complexity, Electron. Trans. Numer. Anal., vol. 30, pp. 291–304 (2008).
  • R.Becker, X.Feng, and A.Prohl, Finite element approximations of the Ericksen-Leslie model for nematic liquid crystal flow, SIAM J. Numer. Anal., vol. 46, no. 4, pp. 1704–1731, (2008).
  • R. Becker and P. Hansbo, A simple pressure stabilization method for the Stokes equation, Comm. Numer. Methods Eng., vol. 24, no. 11, pp. 1421–1430 (2008).
  • R. Becker and B. Vexler, Optimal control of the convection-diffusion equation using stabilized finite element methods, Numer. Math., vol. 106, pp. 349–367 (2007).
  • R. Becker, D. Meidner, and B. Vexler, Efficient numerical solution of parabolic optimization problems by finite element methods, Optimization Methods and Software, vol. 22, no. 5, pp. 813–833 (2007).
  • R.Becker, Estimating the control error in discretized pde-constrained optimization, Journal of Numerical Mathematics, vol. 14, no. 3, pp. 163–185 (2006).
  • R. Becker and B. Vexler, Mesh refinement and numerical sensitivity analysis for parameter calibration of partial differential equations, J. Comp. Phs., vol. 206, no. 1, pp. 95–110, 2005
  • R. Becker, M. Braack, and B. Vexler, Parameter identification for chemical models in combustion problems, Appl. Numer. Math., vol. 54, no. 3-4, pp. 519–536 (2005).
  • P. L. Quere, C. Weisman, H. Paillere, J. Vierendeels, E. Dick, R. Becker, M. Braack, and J. Locke, Modeling of natural convection flows: A benchmark problem for low mach number solvers. part 1. reference solutions, M2AN, vol. 39, no. 3, pp. 609–616 (2005).
  • R. Becker, M. Braack, and B. Vexler, Parameter identification for chemical models in combustion problems, Appl. Numer. Math., vol. 54, no. 3-4, pp. 519–536 (2005).
  • R. Becker and B. Vexler, A posteriori error estimation for finite element discretizations of parameter identification problems, Numer. Math., vol. 96, no. 3, pp. 435–459 (2004).
  • R. Becker, P. Hansbo, and M. G. Larson, Energy norm a posteriori error estimation for discontinuous Galerkin methods, Comput. Methods Appl. Mech. Engrg., vol. 192, pp. 723–733 (2003).
  • R. Becker, P. Hansbo, and R. Stenberg, A finite element method for domain decomposition with non-matching grids, M2AN, vol. 37, no. 2, pp. 209–225 (2003).
  • R. Becker and M. Braack, Solution of a benchmark problem for natural convection with large temperature difference, Int. J. of Therm. Sci., vol. 41, pp. 428–439 (2002).
  • R. Becker, V. Heuveline, and R. Rannacher, An optimal control approach to adaptivity in computational fluid mechanics, Int. J. Numer. Methods Fluids, vol. 40, no. 1-2, pp. 105–120 (2002).
  • R.Becker, Mesh adaptation for Dirichlet flow control via Nitsche’s method, Comm.inNum.Meth.Engrg., vol. 18, pp. 669–680 (2002).
  • R. Becker and M. Braack, A finite element pressure gradient stabilization for the Stokes equations based on local projections, Calcolo, vol. 38, no. 4, pp. 173–199 (2001).
  • R. Becker, Adaptive Finite Elements for Optimal Control Problems, Habilitationsschrift, Institut für Angewandte Mathematik, Universität Heidelberg (2001).
  • R. Becker and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods, Acta Numer., vol. 10, pp. 1–102 (2001).
  • R. Becker, Mesh adaptation for stationary flow control, J. Math. Fluid Mech., vol. 3, no. 4, pp. 317–341 (2001).
  • R. Becker, An optimal control approach to a posteriori error estimation for finite element discretizations of the Navier-Stokes equations, East-West J. Numer. Math., vol. 8, no. 4, pp. 257–342 (2000).
  • R. Becker, H. Kapp, and R. Rannacher, Adaptive finite element methods for optimal control of partial differential equations: Basic concepts, SIAM J. Control Optimization, vol. 39, no. 1, pp. 113–132 (2000).
  • R. Becker and M. Braack, Multigrid techniques for finite elements on locally refined meshes, Numer. Linear Algebra Appl., vol. 7, no. 6, pp. 363–379 (2000).
  • R. Becker, M. Braack, R. Rannacher, and C. Waguet, Fast and reliable solution of the Navier-Stokes equations including chemistry, Comput. Visual. Sci., vol. 2, no. 2 and 3, pp. 107–122 (1999).
  • R. Becker, M. Braack, and R. Rannacher, Numerical simulation of laminar flames at low Mach number with adaptive finite elements, Combust. Theory Modelling, vol. 3, pp. 503–534 (1999).
  • R. Becker and R. Rannacher, A feed-back approach to error control in finite element methods: Basic analysis and examples, East-West J. Numer. Math., vol. 4, pp. 237–264 (1996).
  • R. Becker, C. Johnson, and R. Rannacher, Adaptive error control for multigrid finite element methods, Computing, vol. 55, pp. 271–288 (1995).
  • R. Becker, An Adaptive Finite Element Method for the Incompressible Navier-Stokes Equations on Time-Dependent Domains, PhD thesis, Universität Heidelberg (1995)