Dérivabilité de l'erreur par rapport à la triangulation dans les méthodes d'éléments finis
Déterminants et intégrales de Fresnel
On présente ici une approche directe et géométrique pour le calcul des déterminants d’opérateurs de type Schrödinger sur un graphe fini. Du calcul de l’intégrale de Fresnel associée, on déduit le déterminant. Le calcul des intégrales de Fresnel est grandement facilité par l’utilisation simultanée du théorème de Fubini et d’une version linéaire du calcul symbolique des opérateurs intégraux de Fourier. On obtient de façon directe une formule générale exprimant le déterminant en terme des conditions...
Development of local, global, and trace estimates for the solutions of elliptic equations.
Die maximale Konsistenzordnung von Differenzenapproximationen nichtnegativer Art.
Different types of solvability conditions for differential operators.
Diffusion and propagation problems in some ramified domains with a fractal boundary
This paper is devoted to some elliptic boundary value problems in a self-similar ramified domain of with a fractal boundary. Both the Laplace and Helmholtz equations are studied. A generalized Neumann boundary condition is imposed on the fractal boundary. Sobolev spaces on this domain are studied. In particular, extension and trace results are obtained. These results enable the investigation of the variational formulation of the above mentioned boundary value problems. Next, for homogeneous...
Diffusion processes and second order elliptic operators with singular coefficients for lower order terms.
Direct and Inverse Error Estimates for Finite Elements With Mesh Refinements.
Dirichlet forms for general Wentzell boundary conditions, analytic semigroups, and cosine operator functions.
Dirichlet problem. Characterization of regularity.
Dirichlet problem for a linear elliptic equation in unbounded domains with -boundary data
Dirichlet problems for general Monge-Ampere equations.
Dirichlet problems for semilinear elliptic equations with a fast growth coefficient on unbounded domains.
Dirichlet problems with singular and gradient quadratic lower order terms
We present a revisited form of a result proved in [Boccardo, Murat and Puel, Portugaliae Math.41 (1982) 507–534] and then we adapt the new proof in order to show the existence for solutions of quasilinear elliptic problems also if the lower order term has quadratic dependence on the gradient and singular dependence on the solution.
Dirichlet problems without convexity assumption
We deal with the existence of solutions of the Dirichlet problem for sublinear and superlinear partial differential inclusions considered as generalizations of the Euler-Lagrange equation for a certain integral functional without convexity assumption. We develop a duality theory and variational principles for this problem. As a consequence of the duality theory we give a numerical version of the variational principles which enables approximation of the solution for our problem.
Discontinuous Galerkin methods for problems with Dirac delta source∗
In this article we study discontinuous Galerkin finite element discretizations of linear second-order elliptic partial differential equations with Dirac delta right-hand side. In particular, assuming that the underlying computational mesh is quasi-uniform, we derive an a priori bound on the error measured in terms of the L2-norm. Additionally, we develop residual-based a posteriori error estimators that can be used within an adaptive mesh refinement ...
Discontinuous Galerkin methods for problems with Dirac delta source∗
In this article we study discontinuous Galerkin finite element discretizations of linear second-order elliptic partial differential equations with Dirac delta right-hand side. In particular, assuming that the underlying computational mesh is quasi-uniform, we derive an a priori bound on the error measured in terms of the L2-norm. Additionally, we develop residual-based a posteriori error estimators that can be used within an adaptive mesh refinement ...
Discrete Sobolev and Poincaré inequalities for piecewise polynomial functions.
Discrete Sobolev inequalities and error estimates for finite volume solutions of convection diffusion equations
The topic of this work is to obtain discrete Sobolev inequalities for piecewise constant functions, and to deduce error estimates on the approximate solutions of convection diffusion equations by finite volume schemes.
Discrete Sobolev inequalities and Lp error estimates for finite volume solutions of convection diffusion equations
The topic of this work is to obtain discrete Sobolev inequalities for piecewise constant functions, and to deduce Lp error estimates on the approximate solutions of convection diffusion equations by finite volume schemes.