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.
Analysis of the Schwarz algorithm for mixed finite elements methods
Analysis of two-dimensional FETI-DP preconditioners by the standard additive Schwarz framework.
Anisotropic mesh adaption: application to computational fluid dynamics
In this communication we focus on goal-oriented anisotropic adaption techniques. Starting point has been the derivation of suitable anisotropic interpolation error estimates for piecewise linear finite elements, on triangular grids in . Then we have merged these interpolation estimates with the dual-based a posteriori error analysis proposed by R. Rannacher and R. Becker. As examples of this general anisotropic a posteriori analysis, elliptic, advection-diffusion-reaction and the Stokes problems...
Another approach to vibration analysis of stepped structures.
(A,O)-эллиптические уравнения со слабым вырождением
Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering
This paper addresses some results on the development of an approximate method for computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressible fluid. The basic idea of the method consists in using on-surface differential operators that locally reproduce the interior propagation phenomenon. This approach leads to integral equation formulations with a reduced computational cost compared to standard integral formulations coupling both the transmitted...
Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering
This paper addresses some results on the development of an approximate method for computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressible fluid. The basic idea of the method consists in using on-surface differential operators that locally reproduce the interior propagation phenomenon. This approach leads to integral equation formulations with a reduced computational cost compared to standard integral formulations coupling both the transmitted...
Approximation d'un problème aux limites elliptique d'ordre deux par éléments finis rationnels de Wachspress avec intégration numérique
Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity
We show that the critical nonlinear elliptic Neumann problem in , in , on , where is a bounded and smooth domain in , has arbitrarily many solutions, provided that is small enough. More precisely, for any positive integer , there exists such that for , the above problem has a nontrivial solution which blows up at interior points in , as . The location of the blow-up points is related to the domain geometry. The solutions are obtained as critical points of some finite-dimensional...
Asymmetric elliptic problems with indefinite weights
Asymptotic analysis and sign-changing bubble towers for Lane–Emden problems
We consider the semilinear Lane–Emden problem where and is a smooth bounded domain of . The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of , as . Among other results we show, under some symmetry assumptions on , that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as , and the limit profile looks like a tower of two bubbles given by a superposition of a regular and a singular solution of the Liouville...
Asymptotic analysis of a nonlinear partial differential equation in a semicylinder
Asymptotic analysis of two elliptic equations with oscillating terms
Asymptotic and numerical modelling of flows in fractured porous media
This study concerns some asymptotic models used to compute the flow outside and inside fractures in a bidimensional porous medium. The flow is governed by the Darcy law both in the fractures and in the porous matrix with large discontinuities in the permeability tensor. These fractures are supposed to have a small thickness with respect to the macroscopic length scale, so that we can asymptotically reduce them to immersed polygonal fault interfaces and the model finally consists in a coupling between...
Asymptotic behavior of elliptic boundary-value problems with some small coefficients.
Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities
Let , , and . We study, for , the behavior of positive solutions of the problem in , . In particular, we give a positive answer to an open question formulated in a recent paper of the first author.
Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains