Remarques sur les algorithmes de décomposition de domaines
Replicant compression coding in Besov spaces
We present here a new proof of the theorem of Birman and Solomyak on the metric entropy of the unit ball of a Besov space on a regular domain of The result is: if s - d(1/π - 1/p)+> 0, then the Kolmogorov metric entropy satisfies H(ε) ~ ε-d/s. This proof takes advantage of the representation of such spaces on wavelet type bases and extends the result to more general spaces. The lower bound is a consequence of very simple probabilistic exponential inequalities. To prove the upper bound,...
Replicant compression coding in Besov spaces
We present here a new proof of the theorem of Birman and Solomyak on the metric entropy of the unit ball of a Besov space on a regular domain of The result is: if then the Kolmogorov metric entropy satisfies . This...
Reproducing kernel methods for solving linear initial-boundary-value problems.
Reproducing kernel particle method and its modification
Meshless methods have become an effective tool for solving problems from engineering practice in last years. They have been successfully applied to problems in solid and fluid mechanics. One of their advantages is that they do not require any explicit mesh in computation. This is the reason why they are useful in the case of large deformations, crack propagations and so on. Reproducing kernel particle method (RKPM) is one of meshless methods. In this contribution we deal with some modifications...
Residual a posteriori error estimators for contact problems in elasticity
This paper is concerned with the unilateral contact problem in linear elasticity. We define two a posteriori error estimators of residual type to evaluate the accuracy of the mixed finite element approximation of the contact problem. Upper and lower bounds of the discretization error are proved for both estimators and several computations are performed to illustrate the theoretical results.
Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods
We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the simulation...
Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods
We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the simulation...
Residual based a posteriori error estimators for eddy current computation
Residual based a posteriori error estimators for eddy current computation
We consider H(curl;Ω)-elliptic problems that have been discretized by means of Nédélec's edge elements on tetrahedral meshes. Such problems occur in the numerical computation of eddy currents. From the defect equation we derive localized expressions that can be used as a posteriori error estimators to control adaptive refinement. Under certain assumptions on material parameters and computational domains, we derive local lower bounds and a global upper bound for the total error measured in...
Resilient asynchronous primal Schur method
This paper introduces the application of asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, whose asynchronous convergence is established under classical spectral radius conditions. For the usual case where local Schur complement matrices are not constructed, suitable splittings based only on explicitly generated matrices are provided. Numerical experiments are conducted on a supercomputer for both Poisson's...
Résolution d’un problème aux limites dans un ouvert axisymétrique par éléments finis en et séries de Fourier en
Résolution numérique du problème de propagation de la chaleur à une dimension par la méthode itérative de sur-relaxation
Résolution numérique d'un problème d'écoulement subsonique de fluides compressibles
Résolution parallèle de problèmes aux limites non linéaires
Ritz Approximations to Two-Dimensional Boundary Value Problems.
Ritz-Galerkin Approximations in Blending Function Spaces.
Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices
This article discusses the numerical approximation of time dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respect to a large Ginzburg-Landau parameter are established for a semi-discrete in time and a fully discrete approximation scheme. The proofs rely on an asymptotic expansion of the exact solution and a stability result for degree-one Ginzburg-Landau vortices. The error bounds prove that degree-one vortices can be approximated robustly while unstable higher...
Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices
This article discusses the numerical approximation of time dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respect to a large Ginzburg-Landau parameter are established for a semi-discrete in time and a fully discrete approximation scheme. The proofs rely on an asymptotic expansion of the exact solution and a stability result for degree-one Ginzburg-Landau vortices. The error bounds prove that degree-one vortices can be approximated robustly while unstable higher...
Robust domain decomposition preconditioners for abstract symmetric positive definite bilinear forms
An abstract framework for constructing stable decompositions of the spaces corresponding to general symmetric positive definite problems into “local” subspaces and a global “coarse” space is developed. Particular applications of this abstract framework include practically important problems in porous media applications such as: the scalar elliptic (pressure) equation and the stream function formulation of its mixed form, Stokes’ and Brinkman’s equations. The constant in the corresponding abstract...