The analysis of intergrid transfer operators and multigrid methods for nonconforming finite elements.
The boundary value problem for polyanalytic function in multiply-connected region
The coercitivity of elliptic sesquilinear forms on the Sobolev spaces [Abstract of thesis]
The Convergence of Even Degree Spline Collocation Solution for Potential Problems in Smooth Domains of the Plane.
The Dirichlet problem and weighted spaces. I.
The Dirichlet problem for the biharmonic equation in a Lipschitz domain
The Dirichlet problem for the Monge-Ampère equation in convex (but not strictly convex) domains.
The elliptic problems in a family of planar open sets
We propose, on a model case, a new approach to classical results obtained by V. A. Kondrat'ev (1967), P. Grisvard (1972), (1985), H. Blum and R. Rannacher (1980), V. G. Maz'ya (1980), (1984), (1992), S. Nicaise (1994a), (1994b), (1994c), M. Dauge (1988), (1990), (1993a), (1993b), A. Tami (2016), and others, describing the singularities of solutions of an elliptic problem on a polygonal domain of the plane that may appear near a corner. It provides a more precise description of how the solutions...
The general form of local bilinear functions
The scalar product of the FEM basis functions with non-intersecting supports vanishes. This property is generalized and the concept of local bilinear functional in a Hilbert space is introduced. The general form of such functionals in the spaces and is given.
The generalized Riemann-Hilbert boundary value problem for non-homogeneous polyanalytic differential equation of order in the Sobolev space .
The h-p Version of the Finite Element Method for Elliptic Equations of Order 2m.
The multiple layer potential for the biharmonic equation in variables
The definition of multiple layer potential for the biharmonic equation in is given. In order to represent the solution of Dirichlet problem by means of such a potential, a singular integral system, whose symbol determinant identically vanishes, is considered. The concept of bilateral reduction is introduced and employed for investigating such a system.
The -version of the finite element method for elliptic equations of order
The simple layer potential for the biharmonic equation in variables
A theory of the «simple layer potential» for the classical biharmonic problem in is worked out. This hinges on the study of a new class of singular integral operators, each of them trasforming a vector with scalar components into a vector whose components are differential forms of degree one.
The third order spectrum of the p-biharmonic operator with weight
We show that the spectrum of , where , under Navier boundary conditions, contains at least one sequence of eigensurfaces.
Théorème d'indice pour une classe d'opérateurs elliptiques fortement dégénérés sur la frontière
Two-level additive Schwarz preconditioners for fourth-order mixed methods.
Two-sided bounds of eigenvalues of second- and fourth-order elliptic operators
This article presents an idea in the finite element methods (FEMs) for obtaining two-sided bounds of exact eigenvalues. This approach is based on the combination of nonconforming methods giving lower bounds of the eigenvalues and a postprocessing technique using conforming finite elements. Our results hold for the second and fourth-order problems defined on two-dimensional domains. First, we list analytic and experimental results concerning triangular and rectangular nonconforming elements which...