An upper bound for the local time-decay of scattering solutions for the Schrödinger equation with Coulomb potential
An upwind finite element method for singularly perturbed elliptic problems and local estimates in the -norm
Analyse limite d'équations variationnelles dans un domaine contenant une grille
Analyse précisée d'équations semi-linéaires elliptiques sur l'espace hyperbolique et application à la courbure scalaire conforme
Analyse semi-classique de l'effet tunnel
Analyse semi-classique de l'opérateur de Schrödinger sur la sphère
Analyse semi-classique pour l'équation de Harper (avec application à l'équation de Schrödinger avec champ magnétique)
Analyse sur les boules d' un opérateur sous-elliptique.
Analysis of a Damped Nonlinear Multilevel Method.
Analysis of a non-standard mixed finite element method with applications to superconvergence
We show that a non-standard mixed finite element method proposed by Barrios and Gatica in 2007, is a higher order perturbation of the least-squares mixed finite element method. Therefore, it is also superconvergent whenever the least-squares mixed finite element method is superconvergent. Superconvergence of the latter was earlier investigated by Brandts, Chen and Yang between 2004 and 2006. Since the new method leads to a non-symmetric system matrix, its application seems however more expensive...
Analysis of boundary bubbling solutions for an anisotropic Emden–Fowler equation
Analysis of Compatible Discrete Operator schemes for elliptic problems on polyhedral meshes
Compatible schemes localize degrees of freedom according to the physical nature of the underlying fields and operate a clear distinction between topological laws and closure relations. For elliptic problems, the cornerstone in the scheme design is the discrete Hodge operator linking gradients to fluxes by means of a dual mesh, while a structure-preserving discretization is employed for the gradient and divergence operators. The discrete Hodge operator is sparse, symmetric positive definite and is...
Analysis of Finite Element Methods for Second Order Boundary Value Problems Using Mesh Dependent Norms.
Analysis of finite element methods on Bakhvalov-type meshes for linear convection-diffusion problems in 2D
So far optimal error estimates on Bakhvalov-type meshes are only known for finite difference and finite element methods solving linear convection-diffusion problems in the one-dimensional case. We prove (almost) optimal error estimates for problems with exponential boundary layers in two dimensions.
Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control
We study the partial differential equation max{Lu − f, H(Du)} = 0 where u is the unknown function, L is a second-order elliptic operator, f is a given smooth function and H is a convex function. This is a model equation for Hamilton-Jacobi-Bellman equations arising in stochastic singular control. We establish the existence of a unique viscosity solution of the Dirichlet problem that has a Hölder continuous gradient. We also show that if H is uniformly convex, the gradient of this solution...
Analysis of mixed finite element methods on locally refined grids.
Analysis of mixed methods using conforming and nonconforming finite element methods
Analysis of multilevel decomposition iterative methods for mixed finite element methods
Analysis of patch substructuring methods
Patch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains condensated, on the interfaces to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties have not been studied yet. We analyze geometric patch substructuring methods for the special case of one...
Analysis of the finite element method for transmission/mixed boundary value problems on general polygonal domains.