Discontinuous Galerkin approximation of the Laplace eigenproblem, Computer Methods in Applied Mechanics and Engineering, vol.195, pp.3483-3503, 2006. ,
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. ,
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
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
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
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems, SIAM Journal on Numerical Analysis, vol.39, pp.1749-1779, 2002. ,
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
An Interior Penalty Finite Element Method with Discontinuous Elements, SIAM Journal on Numerical Analysis, vol.19, pp.742-760, 1982. ,
L ? -Error Estimates on Graded Meshes with Application to Optimal Control, SIAM Journal on Control and Optimization, vol.48, pp.1771-1796, 2009. ,
,
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. ,
A theoretical investigation of HeH+, Journal of Molecular Spectroscopy, vol.75, pp.462-473, 1979. ,
Zur Quantentheorie der Molekeln, Annalen der Physik, vol.389, pp.457-484, 1927. ,
, The Mathematical theory of finite element methods, vol.46, pp.512-513, 2003.
A perturbationmethod-based a posteriori estimator for the planewave discretization of nonlinear Schrödinger equations, Comptes Rendus Mathematique, vol.352, pp.941-946, 2014. ,
A perturbationmethod-based post-processing for the planewave discretization of Kohn-Sham models, Journal of Computational Physics, vol.307, pp.446-459, 2016. ,
Guaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations, SIAM Journal on Numerical Analysis, vol.55, pp.2228-2254, 2017. ,
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. ,
Numerical Analysis of Nonlinear Eigenvalue Problems, Journal of Scientific Computing, vol.45, pp.90-117, 2010. ,
Crack Singularities for General Elliptic Systems, Mathematische Nachrichten, vol.235, pp.29-49, 2002. ,
Corner singularities and analytic regularity for linear elliptic systems, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00453934
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
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
Weighted analytic regularity in polyhedra, Computers and Mathematics with Applications, vol.67, pp.807-817, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00735620
Exponential convergence of hp-FEM for Maxwell equations with weighted regularization in polygonal domains, Mathematical Models, vol.15, pp.575-622, 2005. ,
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.
Méthodes mathématiques en chimie quantique : une introduction, p.409, 2006. ,
Variational Methods for the Solution of Problems of Equilibrium and Vibrations, Bulletin of the American Mathematical Society, vol.49, pp.1-24, 1943. ,
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems, SIAM Journal on Numerical Analysis, vol.35, pp.2440-2463, 1998. ,
On the Numerical Analysis of Adaptive Spectral/hp Methods for Elliptic Problems, Analysis and Numerics of Partial Differential Equations, vol.4, 2013. ,
Real analyticity away from the nucleus of pseudorelativistic Hartree-Fock orbitals, Analysis & PDE, vol.5, pp.657-691, 2012. ,
, Mathematical Aspects of Discontinuous Galerkin Methods, vol.69, 2012.
Best approximation property in the W 1 ? norm for finite element methods on graded meshes, Mathematics of Computation, vol.81, pp.743-764, 2011. ,
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. ,
A posteriori analysis of a nonlinear Gross-Pitaevskiitype eigenvalue problem, IMA Journal of Numerical Analysis, vol.37, pp.94-137, 2017. ,
On spectral approximation. I. The problem of convergence, RAIRO Analyse Numérique, vol.12, pp.97-112, 1978. ,
On spectral approximation. II. Error estimates for the Galerkin method, RAIRO Analyse Numérique, vol.12, pp.113-119, 1978. ,
, Theory and Practice of Finite Elements, vol.159, 2004.
, Pseudo-Differential Operators, Singularities, Applications. Basel: Birkhäuser Basel, p.349, 1997.
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
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. ,
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. ,
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. ,
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. ,
The h-p version of the finite element method -Part 1: The basic approximation results, Computational Mechanics, vol.1, pp.21-41, 1986. ,
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. ,
Inverse-type estimates on hp-finite element spaces and applications, Mathematics of Computation, vol.77, pp.201-219, 2008. ,
Reliable a-posteriori error estimators for hp-adaptive finite element approximations of eigenvalue/eigenvector problems, 2011. ,
Error control for hp-adaptive approximations of semi-definite eigenvalue problems, Computing (2013), pp.1-31 ,
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. ,
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. ,
Pointwise error estimates for discontinuous Galerkin methods with lifting operators for elliptic problems, Mathematics of Computation, vol.75, pp.1067-1085, 2006. ,
From Euler, Ritz, and Galerkin to Modern Computing, SIAM Review, vol.54, pp.627-666, 2012. ,
Analysis of periodic Schrödinger operators: Regularity and approximation of eigenfunctions, Journal of Mathematical Physics, vol.49, p.83501, 2008. ,
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. ,
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems, ACM Transactions on Mathematical Software, vol.31, pp.351-362, 2005. ,
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. ,
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. ,
, Nodal Discontinuous Galerkin Methods, vol.54, 2008.
Tranformation de Mellin et développements, In: L'Enseignement Mathématique, vol.25, pp.285-308, 1979. ,
The fundamental solution of linear elliptic differential equations with analytic coefficients, Communications on Pure and Applied Mathematics, vol.3, pp.273-304, 1950. ,
New idea for proof of analyticity of solutions to analytic nonlinear elliptic equations, SUT Journal of Mathematics, vol.32, pp.157-161, 1996. ,
Differential Equations with Operator Coefficients, 1999. ,
Elliptic boundary value problems in domains with point singularities, p.414, 1997. ,
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. ,
Handbook of Numerical Analysis, X. Special volume: computational chemistry, p.899, 2003. ,
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
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
Analysis of a modified Schrödinger operator in 2D: Regularity, index, and FEM, Journal of Computational and Applied Mathematics, vol.224, pp.320-338, 2009. ,
Poincaré-type inequalities for broken Sobolev spaces, pp.1-20, 2003. ,
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. ,
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. ,
Asymptotic Theory Elliptic Boundary Value Problems in Singularly Perturbed Domains, vol.1, 2000. ,
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. ,
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. ,
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. ,
Elliptic Equations in Polyhedral Domains, Mathematical Surveys and Monographs. American Mathematical Society, vol.162, 2010. ,
Regularity of the solutions of elliptic systems in polyhedral domains, Bulletin of the Belgian Mathematical Society -Simon Stevin, vol.4, pp.411-429, 1997. ,
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. ,
Bose-Einstein condensation, 2003. ,
Convergence acceleration of iterative sequences. the case of scf iteration, Chemical Physics Letters, vol.73, pp.393-398, 1980. ,
Numerical Models for Differential Problems, vol.16, 2017. ,
Triangular mesh methods for the neutron transport equation, Los Alamos Scientific Lab, 1973. ,
Theorie der Transversalschwingungen einer quadratischen Platte mit freien Rändern, Annalen der Physik, vol.333, pp.737-786, 1909. ,
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. ,
Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations, Society for Industrial and Applied Mathematics, 2008. ,
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. ,
An Undulatory Theory of the Mechanics of Atoms and Molecules, Physical Review, vol.28, pp.1049-1070, 1926. ,
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. ,
An analysis of the finite element method. Second, p.402, 2008. ,
Modern quantum chemistry: introduction to advanced electronic structure theory, 2012. ,
hp-dGFEM for second order elliptic problems in polyhedra. II: Exponential convergence, SIAM Journal on Numerical Analysis, vol.51, pp.2005-2035, 2013. ,
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. ,
hp-dGFEM for second-order mixed elliptic problems in polyhedra, Mathematics of Computation, vol.85, pp.1051-1083, 2016. ,
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. ,
A Krylov-Schur Algorithm for Large Eigenproblems, SIAM Journal on Matrix Analysis and Applications, vol.23, pp.601-614, 2002. ,
A Jacobi-Davidson Iteration Method for Linear Eigenvalue Problems, SIAM Journal on Matrix Analysis and Applications, vol.17, pp.401-425, 1996. ,
BiCGstab(l) and other hybrid Bi-CG methods, Numerical Algorithms, vol.7, pp.75-109, 1994. ,
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
Maximum Norm Estimates in the Finite Element Method on Plane Polygonal Domains. Part 1, Mathematics of Computation, vol.32, pp.73-109, 1978. ,
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. ,
An Elliptic Collocation-Finite Element Method with Interior Penalties, SIAM Journal on Numerical Analysis, vol.15, pp.152-161, 1978. ,
Weighted L2-norm a posteriori error estimation of FEM in polygons, International Journal of Numerical Analysis and Modeling, vol.4, pp.100-115, 2007. ,