Transposition des problèmes aux limites elliptiques
Transposition des problèmes aux limites elliptiques
Two Families of Mixed Finite Elements for Second Order Elliptic Problems.
Two Methods of Solution of the Three-Dimensional Inverse Nodal Problem.
The operator with the Dirichlet boundary condition is considered in a parallelepiped. The problem of restoring from positions of nodal surfaces is solved.
Two preconditioners based on the multi-level splitting of finite element spaces.
Two solutions for a nonlinear Dirichlet problem with positive forcing
Given a semilinear elliptic boundary value problem having the zero solution and where the nonlinearity crosses the first eigenvalue, we perturb it by a positive forcing term; we show the existence of two solutions under certain conditions that can be weakened in the onedimensional case.
Two-sided a posteriori error estimates for linear elliptic problems with mixed boundary conditions
The paper is devoted to verification of accuracy of approximate solutions obtained in computer simulations. This problem is strongly related to a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain where such errors are too large and certain mesh refinements should be performed. A mathematical model consisting of a linear elliptic (reaction-diffusion) equation with a mixed Dirichlet/Neumann/Robin boundary condition is considered...
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...
Two-sided bounds of the discretization error for finite elements
We derive an optimal lower bound of the interpolation error for linear finite elements on a bounded two-dimensional domain. Using the supercloseness between the linear interpolant of the true solution of an elliptic problem and its finite element solution on uniform partitions, we further obtain two-sided a priori bounds of the discretization error by means of the interpolation error. Two-sided bounds for bilinear finite elements are given as well. Numerical tests illustrate our theoretical analysis....
Two-sided bounds of the discretization error for finite elements
We derive an optimal lower bound of the interpolation error for linear finite elements on a bounded two-dimensional domain. Using the supercloseness between the linear interpolant of the true solution of an elliptic problem and its finite element solution on uniform partitions, we further obtain two-sided a priori bounds of the discretization error by means of the interpolation error. Two-sided bounds for bilinear finite elements are given as well. Numerical tests illustrate our theoretical analysis. ...
Über das Spektrum des Laplace-Operators in einigen unbeschränkten Gebieten.
Über eine Eigenschaft der verallgemeinerten Lösung des Poissonschen Problems (Vorläufige Mitteilung)
Un problema di omogeneizzazione bidimensionale
In this note we study the periodic homogenization problem for a particular bidimensional selfadjoint elliptic operator of the second order. Theoretical and numerical considerations allow us to conjecture explicit formulae for the coefficients of the homogenized operator.
Une classification de problèmes elliptiques dégénérés à une ou plusieurs variables
Une inégalité universelle pour la première valeur propre du laplacien
Une méthode nodale appliquée à un problème de diffusion à coefficients généralisés
Une méthode nodale appliquée à un problème de diffusion à coefficients généralisés
In this paper, we consider second order neutrons diffusion problem with coefficients in L∞(Ω). Nodal method of the lowest order is applied to approximate the problem's solution. The approximation uses special basis functions [1] in which the coefficients appear. The rate of convergence obtained is O(h2) in L2(Ω), with a free rectangular triangulation.
Unique continuation from Cauchy data in unknown non-smooth domains
We consider a conducting body which presents some (unknown) perfectly insulating defects, such as cracks or cavities, for instance. We perform measurements of current and voltage type on a (known) part of the boundary of the conductor. We prove that, even if the defects are unknown, the current and voltage measurements at the boundary uniquely determine the corresponding electrostatic potential inside the conductor. A corresponding stability result, related to the stability of Neumann problems with...
Uniqueness for a boundary identification problem in thermal imaging.
Uniqueness for positive solutions of -Laplacian problem in an annulus