Hodge theory in the Sobolev topology for the de Rham complex on a smoothly bounded domain in Euclidean space.
Hölder regularity of solutions to second-order elliptic equations in nonsmooth domains.
Homogénéisation et perturbations dans un problème lié à l'échauffement d'un câble électrique
Homogenization in chemical reactive flows.
Homogenization of constrained optimal control problems for one-dimensional elliptic equations on periodic graphs
We are concerned with the asymptotic analysis of optimal control problems for -D partial differential equations defined on a periodic planar graph, as the period of the graph tends to zero. We focus on optimal control problems for elliptic equations with distributed and boundary controls. Using approaches of the theory of homogenization we show that the original problem on the periodic graph tends to a standard linear quadratic optimal control problem for a two-dimensional homogenized system, and...
Homogenization of constrained optimal control problems for one-dimensional elliptic equations on periodic graphs
We are concerned with the asymptotic analysis of optimal control problems for 1-D partial differential equations defined on a periodic planar graph, as the period of the graph tends to zero. We focus on optimal control problems for elliptic equations with distributed and boundary controls. Using approaches of the theory of homogenization we show that the original problem on the periodic graph tends to a standard linear quadratic optimal control problem for a two-dimensional homogenized system,...
Homogenization with uncertain input parameters
We homogenize a class of nonlinear differential equations set in highly heterogeneous media. Contrary to the usual approach, the coefficients in the equation characterizing the material properties are supposed to be uncertain functions from a given set of admissible data. The problem with uncertainties is treated by means of the worst scenario method, when we look for a solution which is critical in some sense.
Homotopical Linking and Morse Index estimates in Min-max Theroems.
HP-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form
We propose and analyze a domain decomposition method on non-matching grids for partial differential equations with non-negative characteristic form. No weak or strong continuity of the finite element functions, their normal derivatives, or linear combinations of the two is imposed across the boundaries of the subdomains. Instead, we employ suitable bilinear forms defined on the common interfaces, typical of discontinuous Galerkin approximations. We prove an error bound which is optimal with respect...
Hybrid model for the Coupling of an Asymptotic Preserving scheme with the Asymptotic Limit model: The One Dimensional Case⋆
In this paper a strategy is investigated for the spatial coupling of an asymptotic preserving scheme with the asymptotic limit model, associated to a singularly perturbed, highly anisotropic, elliptic problem. This coupling strategy appears to be very advantageous as compared with the numerical discretization of the initial singular perturbation model or the purely asymptotic preserving scheme introduced in previous works [3, 5]. The model problem addressed...
Identification of cracks with non linear impedances
We consider the inverse problem of determining a crack submitted to a non linear impedance law. Identifiability and local Lipschitz stability results are proved for both the crack and the impedance.
Identification of cracks with non linear impedances
We consider the inverse problem of determining a crack submitted to a non linear impedance law. Identifiability and local Lipschitz stability results are proved for both the crack and the impedance.
Identification of critical curves. II. Discretization and numerical realization
We consider the finite element approximation of the identification problem, where one wishes to identify a curve along which a given solution of the boundary value problem possesses some specific property. We prove the convergence of FE-approximation and give some results of numerical tests.
Implicit a posteriori error estimation using patch recovery techniques
We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient averaging...
Incremental unknowns for solving partial differential equations.
Incremental unknowns method and compact schemes
Incremental unknowns on nonuniform meshes
Infinite multiplicity of positive solutions for singular nonlinear elliptic equations with convection term and related supercritical problems.
Infinitely many solutions for a Robin boundary value problem.
Infinitely many weak solutions for a -Laplacian equation with nonlinear boundary conditions.