P. F. Antonietti, A. Buffa, and I. Perugia, Discontinuous Galerkin approximation of the Laplace eigenproblem, Computer Methods in Applied Mechanics and Engineering, vol.195, pp.3483-3503, 2006.

M. Ainsworth and D. Kay, The approximation theory for the p-version finite element method and application to non-linear elliptic PDEs, Numerische Mathematik, vol.82, pp.351-388, 1999.

P. R. Amestoy, I. S. Duff, J. Koster, and J. Excellent, A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling, SIAM Journal on Matrix Analysis and Applications, vol.23, pp.15-41, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00808293

B. Ammann and V. Nistor, Weighted Sobolev spaces and regularity for polyhedral domains, Computer Methods in Applied Mechanics and Engineering, vol.196, pp.3650-3659, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00090987

J. Adler and V. Nistor, Graded mesh approximation in weighted Sobolev spaces and elliptic equations in 2D, Mathematics of Computation, vol.84, pp.2191-2220, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01279253

D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini, Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems, SIAM Journal on Numerical Analysis, vol.39, pp.1749-1779, 2002.

D. Arndt, W. Bangerth, D. Davydov, T. Heister, L. Heltai et al., The deal.II Library, Version 8.5, Journal of Numerical Mathematics, vol.25, pp.137-145, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02414571

D. N. Arnold, An Interior Penalty Finite Element Method with Discontinuous Elements, SIAM Journal on Numerical Analysis, vol.19, pp.742-760, 1982.

T. Apel, A. Rösch, and D. Sirch, L ? -Error Estimates on Graded Meshes with Application to Optimal Control, SIAM Journal on Control and Optimization, vol.48, pp.1771-1796, 2009.

S. Balay, S. Abhyankar, M. Adams, J. Brown, P. Brune et al.,

C. Bunge, J. Barrientos, and A. Bunge, Roothaan-Hartree-Fock Ground-State Atomic Wave Functions: Slater-Type Orbital Expansions and Expectation Values for Z = 2-54, Atomic Data and Nuclear Data Tables, vol.53, pp.113-162, 1993.

D. M. Bishop and L. M. Cheung, A theoretical investigation of HeH+, Journal of Molecular Spectroscopy, vol.75, pp.462-473, 1979.

M. Born and R. Oppenheimer, Zur Quantentheorie der Molekeln, Annalen der Physik, vol.389, pp.457-484, 1927.

S. Brenner and L. R. Scott, The Mathematical theory of finite element methods, vol.46, pp.512-513, 2003.

É. Cancès, G. Dusson, Y. Maday, B. Stamm, and M. Vohral?k, A perturbationmethod-based a posteriori estimator for the planewave discretization of nonlinear Schrödinger equations, Comptes Rendus Mathematique, vol.352, pp.941-946, 2014.

E. Cancès, G. Dusson, Y. Maday, B. Stamm, and M. Vohral?k, A perturbationmethod-based post-processing for the planewave discretization of Kohn-Sham models, Journal of Computational Physics, vol.307, pp.446-459, 2016.

E. Cancès, G. Dusson, Y. Maday, B. Stamm, and M. Vohral?k, Guaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations, SIAM Journal on Numerical Analysis, vol.55, pp.2228-2254, 2017.

Z. Chen and H. Chen, Pointwise error estimates of discontinuous Galerkin methods with penalty for second-order elliptic problems, SIAM Journal on Numerical Analysis, vol.151, pp.859-60, 2004.

E. Cancès, R. Chakir, and Y. Maday, Numerical Analysis of Nonlinear Eigenvalue Problems, Journal of Scientific Computing, vol.45, pp.90-117, 2010.

M. Costabel and M. Dauge, Crack Singularities for General Elliptic Systems, Mathematische Nachrichten, vol.235, pp.29-49, 2002.

M. Costabel, M. Dauge, and S. Nicaise, Corner singularities and analytic regularity for linear elliptic systems, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00453934

M. Costabel, M. Dauge, and S. Nicaise, Mellin Analysis of Weighted Sobolev Spaces with Nonhomogeneous Norms on Cones, Around the Research of Vladimir Maz'ya I, pp.105-136, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00402645

M. Costabel, M. Dauge, and S. Nicaise, Analytic Regularity for Linear Elliptic Systems in Polygons and Polyhedra, Mathematical Models and Methods in Applied Sciences, vol.22, p.1250015, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00454133

M. Costabel, M. Dauge, and S. Nicaise, Weighted analytic regularity in polyhedra, Computers and Mathematics with Applications, vol.67, pp.807-817, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00735620

M. Costabel, M. Dauge, and C. Schwab, Exponential convergence of hp-FEM for Maxwell equations with weighted regularization in polygonal domains, Mathematical Models, vol.15, pp.575-622, 2005.

E. Cancès and C. L. Bris, On the convergence of SCF algorithms for the Hartree-Fock equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.34, pp.749-774, 2002.

, Handbook of Numerical Analysis, II. Finite element methods, Handbook of numerical analysis, vol.II, p.928, 1991.

, Handbook of Numerical Analysis, IV. Finite element methods. Part 2. Numerical methods for solids, Handbook of numerical analysis, vol.IV, p.974, 1996.

E. Cancès, C. L. Bris, and Y. Maday, Méthodes mathématiques en chimie quantique : une introduction, p.409, 2006.

R. Courant, Variational Methods for the Solution of Problems of Equilibrium and Vibrations, Bulletin of the American Mathematical Society, vol.49, pp.1-24, 1943.

B. Cockburn and C. Shu, The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems, SIAM Journal on Numerical Analysis, vol.35, pp.2440-2463, 1998.

C. Canuto and M. Verani, On the Numerical Analysis of Adaptive Spectral/hp Methods for Elliptic Problems, Analysis and Numerics of Partial Differential Equations, vol.4, 2013.

A. Dall'acqua, S. Fournais, T. Ø. Sørensen, and E. Stockmeyer, Real analyticity away from the nucleus of pseudorelativistic Hartree-Fock orbitals, Analysis & PDE, vol.5, pp.657-691, 2012.

D. A. Di-pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods, vol.69, 2012.

A. Demlow, D. Leykekhman, A. H. Schatz, and L. B. Wahlbin, Best approximation property in the W 1 ? norm for finite element methods on graded meshes, Mathematics of Computation, vol.81, pp.743-764, 2011.

V. Dolej??, A. Ern, and M. Vohral?k, hp-Adaptation Driven by Polynomial-Degree-Robust A Posteriori Error Estimates for Elliptic Problems, SIAM Journal on Scientific Computing, vol.38, pp.3220-3246, 2016.

G. Dusson and Y. Maday, A posteriori analysis of a nonlinear Gross-Pitaevskiitype eigenvalue problem, IMA Journal of Numerical Analysis, vol.37, pp.94-137, 2017.

J. Descloux, N. Nassif, and J. Rappaz, On spectral approximation. I. The problem of convergence, RAIRO Analyse Numérique, vol.12, pp.97-112, 1978.

J. Descloux, N. Nassif, and J. Rappaz, On spectral approximation. II. Error estimates for the Galerkin method, RAIRO Analyse Numérique, vol.12, pp.113-119, 1978.

A. Ern and J. Guermond, Theory and Practice of Finite Elements, vol.159, 2004.

Y. V. Egorov and B. Schulze, Pseudo-Differential Operators, Singularities, Applications. Basel: Birkhäuser Basel, p.349, 1997.

A. Ern and M. Vohralik, Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous galerkin, and mixed discretizations, SIAM Journal on Numerical Analysis, vol.53, pp.1058-1081, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00921583

B. G. Galerkin, Rods and plates. Series occurring in various questions concerning the elastic equilibrium of rods and plates, In: Engineers Bulletin (Vestnik Inzhenerov), vol.19, pp.897-908, 1915.

W. Gui and I. Babu?ka, The h, p and h-p versions of the finite element method in 1 dimension. Part I. The Error Analysis of the p-Version, Numerische Mathematik, vol.612, pp.577-612, 1986.

W. Gui and I. Babu?ka, The h, p and h-p versions of the finite element method in 1 dimension. Part II. The Error analysis of the h? and h ? p versions, Numerische Mathematik, vol.49, pp.613-657, 1986.

W. Gui and I. Babu?ka, The h, p and h-p versions of the finite element method in 1 dimension. Part III. The Adaptive h-p Version, Numerische Mathematik, vol.683, pp.659-683, 1986.

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

B. Guo and I. Babu?ka, The h-p version of the finite element method -Part 2: General results and applications, In: Computational Mechanics, vol.1, issue.3, pp.203-220, 1986.

E. H. Georgoulis, Inverse-type estimates on hp-finite element spaces and applications, Mathematics of Computation, vol.77, pp.201-219, 2008.

S. Giani, L. Grubi?i?, and J. Ovall, Reliable a-posteriori error estimators for hp-adaptive finite element approximations of eigenvalue/eigenvector problems, 2011.

S. Giani, L. Grubi?i?, and J. Ovall, Error control for hp-adaptive approximations of semi-definite eigenvalue problems, Computing (2013), pp.1-31

S. Giani and E. J. Hall, An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems, Mathematical Models and Methods in Applied Sciences, vol.22, p.1250030, 2012.

E. Georgoulis and E. Süli, Optimal error estimates for the hp-version interior penalty discontinuous Galerkin finite element method, IMA Journal of Numerical Analysis, vol.03, pp.1-17, 2005.

J. Guzmán, Pointwise error estimates for discontinuous Galerkin methods with lifting operators for elliptic problems, Mathematics of Computation, vol.75, pp.1067-1085, 2006.

M. J. Gander and G. Wanner, From Euler, Ritz, and Galerkin to Modern Computing, SIAM Review, vol.54, pp.627-666, 2012.

E. Hunsicker, V. Nistor, and J. O. Sofo, Analysis of periodic Schrödinger operators: Regularity and approximation of eigenfunctions, Journal of Mathematical Physics, vol.49, p.83501, 2008.

P. Houston, Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: the scalar case, IMA Journal of Numerical Analysis, vol.25, pp.726-749, 2005.

V. Hernandez, J. E. Roman, and V. Vidal, SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems, ACM Transactions on Mathematical Software, vol.31, pp.351-362, 2005.

P. Houston, E. Suli, and T. P. Wihler, A posteriori error analysis of hpversion discontinuous Galerkin finite-element methods for second-order quasi-linear elliptic PDEs, IMA Journal of Numerical Analysis, vol.28, pp.245-273, 2007.

P. Houston, D. Schötzau, and T. P. Wihler, Energy norm a posteriori error estimation of hp-adaptive discontinuous Galerkin methods for elliptic problems, Mathematical Models and Methods in Applied Sciences, vol.17, pp.33-62, 2007.

J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods, vol.54, 2008.

P. Jeanquartier, Tranformation de Mellin et développements, In: L'Enseignement Mathématique, vol.25, pp.285-308, 1979.

F. John, The fundamental solution of linear elliptic differential equations with analytic coefficients, Communications on Pure and Applied Mathematics, vol.3, pp.273-304, 1950.

K. Kato, New idea for proof of analyticity of solutions to analytic nonlinear elliptic equations, SUT Journal of Mathematics, vol.32, pp.157-161, 1996.

V. Kozlov and V. Maz'ya, Differential Equations with Operator Coefficients, 1999.

V. Kozlov, V. G. Mazya, and J. Rossmann, Elliptic boundary value problems in domains with point singularities, p.414, 1997.

V. A. Kondrat'ev, Boundary value problems for elliptic equations in domains with conical or angular points, Trudy Moskovskogo Matemati?eskogo Ob??estva, vol.16, pp.209-292, 1967.

C. and L. Bris, Handbook of Numerical Analysis, X. Special volume: computational chemistry, p.899, 2003.

M. Lewin, Solutions of the Multiconfiguration Equations in Quantum Chemistry, Archive for Rational Mechanics and Analysis, vol.171, pp.83-114, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00093510

H. Li, A. Mazzucato, and V. Nistor, Analysis of the finite element method for transmission/mixed boundary value problems on general polygonal domains, Electronic Transactions Numerical Analysis, vol.37, pp.41-69, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01284891

H. Li and V. Nistor, Analysis of a modified Schrödinger operator in 2D: Regularity, index, and FEM, Journal of Computational and Applied Mathematics, vol.224, pp.320-338, 2009.

A. Lasis and E. Suli, Poincaré-type inequalities for broken Sobolev spaces, pp.1-20, 2003.

E. H. Lieb, R. Seiringer, and J. Yngvason, Bosons in a trap: A rigorous derivation of the Gross-Pitaevskii energy functional, The Stability of Matter: From Atoms to Stars, pp.759-771, 2000.

A. Mazzucato and V. Nistor, Well-posedness and regularity for the elasticity equation with mixed boundary conditions on polyhedral domains and domains with cracks, Archive for Rational Mechanics and Analysis, pp.1-45, 2010.

V. G. Maz'ya, S. Nazarov, and B. Plamenevskij, Asymptotic Theory Elliptic Boundary Value Problems in Singularly Perturbed Domains, vol.1, 2000.

V. G. Maz'ya and B. A. Plamenevskii, Estimates of Green's functions and Schauder estimates for solutions of elliptic boundary problems in a dihedral angle, Siberian Mathematical Journal, vol.19, pp.752-764, 1978.

V. G. Maz'ya and B. A. Plamenevskii, On the Asymptotics of the Fundamental Solutions of Elliptic Boundary-Value Problems in Regions with Conical Points, Selecta Mathematica Sovietica, vol.4, pp.363-397, 1985.

V. G. Maz'ya and J. Rossmann, Point estimates for Green's matrix to boundary value problems for second order elliptic systems in a polyhedral cone, ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, vol.82, pp.291-316, 2002.

V. G. Maz'ya and J. Rossmann, Elliptic Equations in Polyhedral Domains, Mathematical Surveys and Monographs. American Mathematical Society, vol.162, 2010.

S. Nicaise, Regularity of the solutions of elliptic systems in polyhedral domains, Bulletin of the Belgian Mathematical Society -Simon Stevin, vol.4, pp.411-429, 1997.

J. Nitsche, On Dirichlet problems using subspaces with nearly zero boundary conditions, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, pp.603-627, 1972.

L. P. Pitaevskii and S. Stringari, Bose-Einstein condensation, 2003.

P. Pulay, Convergence acceleration of iterative sequences. the case of scf iteration, Chemical Physics Letters, vol.73, pp.393-398, 1980.

A. Quarteroni, Numerical Models for Differential Problems, vol.16, 2017.

W. H. Reed and T. Hill, Triangular mesh methods for the neutron transport equation, Los Alamos Scientific Lab, 1973.

W. Ritz, Theorie der Transversalschwingungen einer quadratischen Platte mit freien Rändern, Annalen der Physik, vol.333, pp.737-786, 1909.

W. Ritz, Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik, In: Journal für die reine und angewandte Mathematik, vol.135, pp.1-61, 1909.

B. Rivière, Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations, Society for Industrial and Applied Mathematics, 2008.

A. H. Schatz, Pointwise Error Estimates and Asymptotic Error Expansion Inequalities for the Finite Element Method on Irregular Grids: Part II. Interior Estimates, SIAM Journal on Numerical Analysis, vol.38, pp.1269-1293, 2001.

E. Schrödinger, An Undulatory Theory of the Mechanics of Atoms and Molecules, Physical Review, vol.28, pp.1049-1070, 1926.

A. H. Schatz, Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates, Mathematics of Computation, vol.67, pp.877-900, 1998.

G. Strang and G. Fix, An analysis of the finite element method. Second, p.402, 2008.

A. Szabo and N. Ostlund, Modern quantum chemistry: introduction to advanced electronic structure theory, 2012.

D. Schötzau, C. Schwab, and T. P. Wihler, hp-dGFEM for second order elliptic problems in polyhedra. II: Exponential convergence, SIAM Journal on Numerical Analysis, vol.51, pp.2005-2035, 2013.

D. Schötzau, C. Schwab, and T. Wihler, hp-dGFEM for Second-Order Elliptic Problems in Polyhedra I: Stability on Geometric Meshes, SIAM Journal on Numerical Analysis, vol.51, pp.1610-1633, 2013.

D. Schötzau, C. Schwab, and T. P. Wihler, hp-dGFEM for second-order mixed elliptic problems in polyhedra, Mathematics of Computation, vol.85, pp.1051-1083, 2016.

G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Université de Grenoble. Annales de l'Institut Fourier, vol.15, pp.189-258, 1965.

G. W. Stewart, A Krylov-Schur Algorithm for Large Eigenproblems, SIAM Journal on Matrix Analysis and Applications, vol.23, pp.601-614, 2002.

G. L. Sleijpen, H. A. Van-der, and . Vorst, A Jacobi-Davidson Iteration Method for Linear Eigenvalue Problems, SIAM Journal on Matrix Analysis and Applications, vol.17, pp.401-425, 1996.

G. L. Sleijpen, H. A. Van-der, D. R. Vorst, and . Fokkema, BiCGstab(l) and other hybrid Bi-CG methods, Numerical Algorithms, vol.7, pp.75-109, 1994.

B. Stamm and T. P. Wihler, hp-optimal discontinuous Galerkin methods for linear elliptic problems, Mathematics of Computation, vol.79, pp.2117-2133, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01090918

A. H. Schatz and L. B. Wahlbin, Maximum Norm Estimates in the Finite Element Method on Plane Polygonal Domains. Part 1, Mathematics of Computation, vol.32, pp.73-109, 1978.

H. A. Van-der and . Vorst, Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems, SIAM Journal on Scientific and Statistical Computing, vol.13, pp.631-644, 1992.

M. F. Wheeler, An Elliptic Collocation-Finite Element Method with Interior Penalties, SIAM Journal on Numerical Analysis, vol.15, pp.152-161, 1978.

T. Wihler, Weighted L2-norm a posteriori error estimation of FEM in polygons, International Journal of Numerical Analysis and Modeling, vol.4, pp.100-115, 2007.