We consider the numerical approximation of singularly perturbed elliptic problems in smooth domains. The solution to such problems can be decomposed into a smooth part and a boundary layer part. We present guidelines for the eeective resolution of boundary layers in the context of the hp nite element method and we construct tensor product spaces that approximate these layers uniformly at a near...

Charles[1] proved the convergence of Picard-type iterative for generalized Φ− accretive non-self maps in a real uniformly smooth Banach space. Based on theorems zeros strongly quasi- and fixed points hemi-contractions, we extend results to Ishikawa iteration process with er- rors hemi-contractive .

We consider the stochastic Allen-Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension d ≤ 3, and study the semidiscretization in time of the equation by an implicit Euler method. We show that the method converges pathwise with a rate O(∆tγ) for any γ < 1 2 . We also prove that the scheme converges uniformly in the strong Lp-sense but wi...

We prove the existence of piecewise polynomials strictly convex smooth functions which converge uniformly on compact subsets to the Aleksandrov solution of the Monge-Ampère equation. We extend the Aleksandrov theory to right hand side only locally integrable and on convex bounded domains not necessarily strictly convex. The result suggests that for the numerical resolution of the equation, it i...

We consider the numerical approximation of singularly perturbed elliptic boundary value problems over non-smooth domains. We use a decomposition of the solution that contains a smooth part, a corner layer part and a boundary layer part. Explicit guidelines for choosing mesh-degree combinations are given that yield nite element spaces with robust approximation properties. In particular, we const...

In this paper, we consider a modified projective algorithm for finding common elements of the set of common fixed points of a finite family of quasi-φ-nonexpansive mappings and the set of solutions of an equilibrium problem in uniformly smooth and strictly convex Banach spaces with the property(K). Our results improve and extend the corresponding results announced by many others. AMS subject cl...

We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality, the set of solutions of the generalizedmixed equilibrium problem, and zeros of maximal monotone operators in a Banach space. We obtain a strong convergence theorem for the sequences g...

In this paper, we introduce a new type of a projective algorithm for a pair of quasi-φ-nonexpansive mappings. We establish strong convergence theorems of common fixed points in uniformly smooth and strictly convex Banach spaces with the property(K). Our results improve and extend the corresponding results announced by many others. AMS subject classifications: 47H09, 47H10