I. Babu?ka, B. Szabo, and I. Katz, The p-version of the finite element method, SIAM Journal on Numerical Analysis, vol.18, issue.3, pp.515-545, 1981.

B. Guo and I. Babu?ka, The h-p version of the finite element method, Computational Mechanics, vol.1, issue.1, pp.21-41, 1986.

L. Demkowicz, One and two dimensional elliptic and Maxwell problems, Computing with hp-adaptive finite elements, vol.1, 2007.

L. Demkowicz, J. Kurtz, D. Pardo, M. Paszy?ski, W. Rachowicz et al., Frontiers: three dimensional elliptic and Maxwell problems with applications, Applied Mathematics and Nonlinear Science Series, vol.2, 2008.

J. Schöberl, Netgen an advancing front 2d/3d-mesh generator based on abstract rules, Computing and Visualization in Science, vol.1, issue.1, pp.41-52, 1997.

A. Szymczak, A. Paszy?ska, M. Paszy?ski, and D. Pardo, Preventing deadlock during anisotropic 2D mesh adaptation in hpadaptive FEM, Adaptive Algorithms, ?1.77 17: 3D shock problem: Solution computed on the final adapted hp mesh, vol.4, pp.170-179, 2013.

, ods in Applied Mechanics and Engineering, vol.310, pp.252-277, 2016.

N. D. Zander, Multi-level hp-fem: dynamically changing high-order mesh refinement with arbitrary hanging nodes, 2017.

J. N. Jomo, N. Zander, M. Elhaddad, A. Özcan, S. Kollmannsberger et al., Parallelization of the multi-level hp-adaptive finite cell method, vol.74, pp.126-142, 2017.

, European Seminar on Computing ESCO, 2016.

P. D. Stolfo, A. Schröder, N. Zander, and S. Kollmannsberger, An easy treatment of hanging nodes in hp-finite elements, Finite Elements in, Analysis and Design, vol.121, pp.101-117, 2016.

M. Ainsworth and B. Senior, An adaptive refinement strategy for hp-finite element computations, Applied Numerical Mathematics, vol.26, issue.1, pp.165-178, 1998.

J. Oden and A. Patra, A parallel adaptive strategy for hp finite element computations, Computer Methods in Applied Mechanics and Engineering, vol.121, issue.1, pp.449-470, 1995.

L. Demkowicz, W. Rachowicz, and P. Devloo, Proceedings of the Fifth International Conference on Spectral and High Order Methods (ICOSAHOM-01) (Uppsala), vol.17, pp.117-142, 2002.

D. Pardo, Integration of hp-adaptivity with a two grid solver: applications to electromagnetics, 2004.

M. Paszy?ski, L. Demkowicz, and D. Pardo, Verification of goal-oriented hp-adaptivity, Comput. Math. Appl, vol.50, issue.8-9, pp.1395-1404, 2005.

D. Pardo, L. García-castillo, L. Demkowicz, and C. Torres-verdín, A two-dimensional self-adaptive hp finite element method for the characterization of waveguide discontinuities. II. Goal-oriented hp-adaptivity, Comput. Methods Appl. Mech. Engrg, vol.196, pp.4811-4822, 2007.

L. E. García-castillo, D. Pardo, I. Gómez-revuelto, and L. F. Demkowicz, A two-dimensional self-adaptive hp finite element method for the characterization of waveguide discontinuities. I. Energy-norm based automatic hp-adaptivity, Comput. Methods Appl. Mech. Engrg, vol.196, pp.4823-4852, 2007.

D. Pardo, L. Demkowicz, C. Torres-verdín, and C. Michler, PML enhanced with a self-adaptive goal-oriented hp-finite element method: simulation of through-casing borehole resistivity measurements, SIAM J. Sci. Comput, vol.30, issue.6, pp.2948-2964, 2008.

L. E. Garcia-castillo, D. Pardo, and L. F. Demkowicz, Energy-norm-based and goal-oriented automatic adaptivity for electromagnetics: Application to waveguide discontinuities, Microwave Theory and Techniques, IEEE Transactions on, vol.56, issue.12, pp.3039-3049, 2008.

D. Pardo, Multigoal-oriented adaptivity for hp-finite element methods, Procedia Computer Science, vol.1, issue.1, pp.1953-1961, 2010.

V. M. Calo, D. Pardo, and M. R. Paszy?ski, Goal-oriented self-adaptive hp finite element simulation of 3D DC borehole resistivity simulations, proceedings of the International Conference on Computational Science, ICCS 2011, vol.4, pp.1485-1495, 2011.

I. Gomez-revuelto, L. E. Garcia-castillo, S. Llorente-romano, and D. Pardo, A three-dimensional self-adaptive hp finite element method for the characterization of waveguide discontinuities, Comput. Methods Appl. Mech. Engrg, vol.249, pp.62-74, 2012.

M. Paszy?ski, D. Pardo, and V. Calo, Parallel simulations of 3D DC borehole resistivity measurements with goal-oriented self-adaptive hp finite element method, Journal of the Serbian Society for Computational Mechanics, vol.6, issue.2, pp.1-18, 2012.

J. Alvarez-aramberri, D. Pardo, and H. Barucq, Inversion of magnetotelluric measurements using multigoal oriented hpadaptivity, Procedia Computer Science, vol.18, pp.1564-1573, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00944838

J. Alvarez-aramberri, D. Pardo, and H. Barucq, A secondary field based hp-Finite Element Method for the simulation of magnetotelluric measurements, Journal of Computational Science, vol.11, pp.137-144, 2015.

P. Houston, B. Senior, and E. Süli, Sobolev regularity estimation for hp-adaptive finite element methods, in: Numerical mathematics and advanced applications, pp.631-656, 2003.

W. F. Mitchell and M. A. Mcclain, A comparison of hp-adaptive strategies for elliptic partial differential equations, ACM Trans. Math. Softw, vol.41, issue.1, 2014.

D. Angella, N. Zander, S. Kollmannsberger, F. Frischmann, E. Rank et al., Multi-level hp-adaptivity and explicit error estimation, Advanced Modeling and Simulation in Engineering Sciences, vol.3, issue.1, p.33, 2016.

N. Zander, M. Ruess, T. Bog, S. Kollmannsberger, and E. Rank, Multi-level hp-adaptivity for cohesive fracture modeling, International Journal for Numerical Methods in Engineering, vol.109, issue.13, pp.1723-1755, 2017.

M. Elhaddad, N. Zander, T. Bog, L. Kudela, S. Kollmannsberger et al., Multilevel hp-finite cell method for embedded interface problems with application in biomechanics, International Journal for Numerical Methods in Biomedical Engineering, vol.34, issue.4, pp.2951-2951, 2018.

S. Kollmannsberger, A. Özcan, M. Carraturo, N. Zander, and E. Rank, A hierarchical computational model for moving thermal loads and phase changes with applications to selective laser melting, Computers & Mathematics with Applications, vol.75, issue.5, pp.1483-1497, 2018.

T. Bog, N. Zander, S. Kollmannsberger, and E. Rank, Weak imposition of frictionless contact constraints on automatically recovered high-order, embedded interfaces using the finite cell method, Computational Mechanics, vol.61, issue.4, pp.385-407, 2018.

I. Babu?ka and W. C. Rheinboldt, A-posteriori error estimates for the finite element method, International Journal for Numerical Methods in Engineering, vol.12, issue.10, pp.1597-1615, 1978.

P. Houston, B. Senior, and E. Süli, hp-discontinuous Galerkin finite element methods for hyperbolic problems: error analysis and adaptivity, iCFD Conference on Numerical Methods for Fluid Dynamics, vol.40, pp.153-169, 2001.

S. Congreve and P. Houston, Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration, Recent advances in scientific computing and applications, vol.586, pp.135-142, 2013.

S. Giani and E. Hall, An a-posteriori error estimate for hp-adaptive DG methods for elliptic eigenvalue problems on anisotropically refined meshes, Computing, vol.95, issue.1, pp.319-341, 2013.

S. Giani, D. Schötzau, and L. Zhu, An a-posteriori error estimate for hp-adaptive DG methods for convection-diffusion problems on anisotropically refined meshes, Comput. Math. Appl, vol.67, issue.4, pp.869-887, 2014.

P. Houston, I. Perugia, and D. Schötzau, Numerical mathematics and advanced applications, pp.785-794, 2003.

A. Cangiani, E. H. Georgoulis, and P. Houston, hp-version discontinuous Galerkin methods on polygonal and polyhedral meshes, vol.24, pp.2009-2041, 2014.

A. Cangiani, Z. Dong, E. H. Georgoulis, and P. Houston, hp-version discontinuous Galerkin methods for advection-diffusionreaction problems on polytopic meshes, ESAIM Math. Model. Numer. Anal, vol.50, issue.3, pp.699-725, 2016.

L. Demkowicz, J. Gopalakrishnan, and A. H. Niemi, A class of discontinuous Petrov-Galerkin methods. Part III: Adaptivity, vol.62, pp.396-427, 2012.

S. Petrides and L. F. Demkowicz, An adaptive DPG method for high frequency time-harmonic wave propagation problems, Computers & Mathematics with Applications, vol.74, issue.8, pp.1999-2017, 2017.

P. Binev, Instance optimality for hp-type approximation, Oberwolfach Reports, vol.39, pp.14-16, 2013.

C. Canuto, R. H. Nochetto, R. Stevenson, and M. Verani, Convergence and optimality of hp-afem, Numer. Math, vol.135, issue.4, pp.1073-1119, 2017.

C. Erath, G. Gantner, and D. Praetorius, Optimal convergence behavior of adaptive FEM driven by simple (h-h/2)-type error estimators, 2018.

W. Rachowicz, D. Pardo, and L. Demkowicz, Fully automatic hp-adaptivity in three dimensions, Comput. Methods Appl. Mech. Engrg, vol.195, pp.4816-4842, 2006.

M. Bürg and W. Dörfler, Convergence of an adaptive hp finite element strategy in higher space-dimensions, Applied Numerical Mathematics, vol.61, issue.11, pp.1132-1146, 2011.

C. Canuto, R. H. Nochetto, R. Stevenson, and M. Verani, On p-robust saturation for hp-AFEM, Comput. Math. Appl, vol.73, issue.9, pp.2004-2022, 2017.

P. Binev, Tree approximation for hp-adaptivity, SIAM Journal on Numerical Analysis, vol.56, issue.6, pp.3346-3357, 2018.

P. Daniel, A. Ern, I. Smears, and M. Vohralík, An adaptive hp-refinement strategy with computable guaranteed bound on the error reduction factor, Computers & Mathematics with Applications, vol.76, issue.5, pp.967-983, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01666763

S. Prudhomme and J. T. Oden, On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors, Comput. Methods Appl. Mech. Engrg, vol.176, issue.1-4, pp.313-331, 1999.

J. T. Oden and S. Prudhomme, Goal-oriented error estimation and adaptivity for the finite element method, Comput. Math. Appl, vol.41, issue.5-6, pp.735-756, 2001.