A. Nealen, Physically Based Deformable Models in Computer Graphics, Computer graphics forum, pp.809-836, 2006.
DOI : 10.1145/1015706.1015733
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.124.4664

Y. Wang, Linear subspace design for real-time shape deformation, ACM Transactions on Graphics, vol.34, issue.4, p.57, 2015.
DOI : 10.1145/2766952

H. Courtecuisse, Real-time simulation of contact and cutting of heterogeneous soft-tissues, Medical Image Analysis, vol.18, issue.2, pp.394-410, 2014.
DOI : 10.1016/j.media.2013.11.001
URL : https://hal.archives-ouvertes.fr/hal-01097108

O. Zienkiewicz, The finite element method: Its basis and fundamentals, 2013.

V. P. Nguyen, Meshless methods: A review and computer implementation aspects, Mathematics and Computers in Simulation, vol.79, issue.3, pp.763-813, 2008.
DOI : 10.1016/j.matcom.2008.01.003
URL : http://orbilu.uni.lu/handle/10993/13726

X. Wu, Adaptive Nonlinear Finite Elements for Deformable Body Simulation Using Dynamic Progressive Meshes, Computer Graphics Forum, pp.349-358, 2001.
DOI : 10.1111/1467-8659.00527

M. Müller, Stable real-time deformations, Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation , SCA '02, pp.49-54, 2002.
DOI : 10.1145/545261.545269

M. Ainsworth and J. T. Oden, A posteriori error estimation in finite element analysis, Computer Methods in Applied Mechanics and Engineering, vol.142, issue.1-2, 2011.
DOI : 10.1016/S0045-7825(96)01107-3

M. Seiler, Robust interactive cutting based on an adaptive octree simulation mesh, The Visual Computer, pp.519-529, 2011.
DOI : 10.1007/s00371-011-0561-3

R. Verfürth, A posteriori error estimation techniques for finite element methods, ser. Numerical Mathematics and Scientific Computation

O. Zienkiewicz and J. Zhu, The superconvergent patch recovery (SPR) and adaptive finite element refinement, Computer Methods in Applied Mechanics and Engineering, vol.101, issue.1-3, pp.207-224, 1992.
DOI : 10.1016/0045-7825(92)90023-D

C. Carstensen and S. Bartels, Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM, Mathematics of Computation, vol.71, issue.239, pp.945-969, 2002.
DOI : 10.1090/S0025-5718-02-01402-3

S. Bartels and C. Carstensen, Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEM, Mathematics of Computation, vol.71, issue.239, pp.971-994, 2002.
DOI : 10.1090/S0025-5718-02-01412-6

I. Babu?ka and W. C. Rheinboldt, Error Estimates for Adaptive Finite Element Computations, SIAM Journal on Numerical Analysis, vol.15, issue.4, pp.736-754, 1978.
DOI : 10.1137/0715049

N. Hamzé, Preoperative trajectory planning for percutaneous procedures in deformable environments, Computerized Medical Imaging and Graphics, vol.47, pp.16-28
DOI : 10.1016/j.compmedimag.2015.10.002

N. Abolhassani, Needle insertion into soft tissue: A survey, Medical Engineering & Physics, vol.29, issue.4, pp.413-431, 2007.
DOI : 10.1016/j.medengphy.2006.07.003

C. Duriez, Interactive Simulation of Flexible Needle Insertions Based on Constraint Models, Lecture Notes in Computer Science, vol.5762, issue.2, pp.291-299, 2009.
DOI : 10.1007/978-3-642-04271-3_36
URL : https://hal.archives-ouvertes.fr/inria-00540334

S. Misra, Mechanics of Flexible Needles Robotically Steered through Soft Tissue, The International Journal of Robotics Research, vol.29, issue.13, pp.1640-1660, 2010.
DOI : 10.1177/0278364910369714

J. Wu, A Survey of Physically Based Simulation of Cuts in Deformable Bodies, Eurographics (State of the Art Reports, pp.1-19, 2014.
DOI : 10.1111/cgf.12528

C. Dick, A Hexahedral Multigrid Approach for Simulating Cuts in Deformable Objects, IEEE Transactions on Visualization and Computer Graphics, vol.17, issue.11, pp.1663-1675, 2011.
DOI : 10.1109/TVCG.2010.268

G. R. Liu and S. S. Quek, Chapter 3 -Fundamentals for Finite Element Method, " in The Finite Element Method, Eds. Oxford: Butterworth- Heinemann, pp.43-79, 2014.

O. Zienkiewicz and R. Taylor, The Finite Element Method: Solid mechanics, ser. Referex collection.Mecánica y materiales, 2000.

C. Felippa and B. Haugen, A unified formulation of small-strain corotational finite elements: I. Theory, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.21-24, pp.2285-2335, 2005.
DOI : 10.1016/j.cma.2004.07.035

A. Pinelli, Immersed-boundary methods for general finite-difference and finite-volume Navier???Stokes solvers, Proceedings of SIGGRAPH, pp.9073-9091, 1998.
DOI : 10.1016/j.jcp.2010.08.021
URL : https://hal.archives-ouvertes.fr/hal-00951516

D. Kwak and Y. Im, Hexahedral mesh generation for remeshing in three-dimensional metal forming analyses, Journal of Materials Processing Technology, vol.138, issue.1-3, pp.531-537, 2003.
DOI : 10.1016/S0924-0136(03)00142-0

D. Koschier, Adaptive Tetrahedral Meshes for Brittle Fracture Simulation, Symposium on Computer Animation The Eurographics Association, 2014.

D. Burkhart, Adaptive and Feature-Preserving Subdivision for High-Quality Tetrahedral Meshes, Computer Graphics Forum, vol.1, issue.3, pp.117-127, 2010.
DOI : 10.1111/j.1467-8659.2009.01581.x
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.685.1843

C. Paulus, Virtual cutting of deformable objects based on efficient topological operations, The Visual Computer, pp.831-841, 2015.
DOI : 10.1007/s00371-015-1123-x
URL : https://hal.archives-ouvertes.fr/hal-01208546

E. Sifakis, Hybrid simulation of deformable solids, Proc. Symposium on Computer Animation, pp.81-90, 2007.

H. Uzawa and K. J. Arrow, Iterative methods for concave programming, Preference, production, and capital, pp.135-148, 1989.
DOI : 10.1017/CBO9780511664496.011

I. Babu?ka, The finite element method with penalty, Mathematics of Computation, vol.27, issue.122, pp.221-228, 1973.
DOI : 10.1090/S0025-5718-1973-0351118-5

P. Papadopoulos and J. M. Solberg, A Lagrange multiplier method for the finite element solution of frictionless contact problems, Mathematical and Computer Modelling, vol.28, issue.4-8, pp.373-384, 1998.
DOI : 10.1016/S0895-7177(98)00128-9

M. Seiler, Enriching coarse interactive elastic objects with high-resolution data-driven deformations, Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp.9-17, 2012.

M. U. Seiler, Efficient Transfer of Contact-Point Local Deformations for Data-Driven Simulations, Workshop on Virtual Reality Interaction and Physical Simulation. The Eurographics Association, 2014.

P. Hauseux, Accelerating Monte Carlo estimation with derivatives of high-level finite element models, Computer Methods in Applied Mechanics and Engineering, vol.318, p.2017
DOI : 10.1016/j.cma.2017.01.041