Ali Souissi

New diffusion models in image processing

We give some diffusion models which can be used for restoration in image processing. The proposed model is a combination of fast growth with respect to low gradient and slow growth when the gradient is large. The existence theorem for solutions and some numerical results are given.

Strengthened Cauchy–Bunyakowski–Schwarz inequality for a three‐dimensional elasticity system

The constant γ of the strengthened Cauchy–Bunyakowski–Schwarz (CBS) inequality plays a fundamental role in the convergence rate of multilevel iterative methods. The main purpose of this work is to give an estimate of the constant γ for a three-dimensional elasticity system. The theoretical results obtained are practically important for the successful implementation of the finite element method to large-scale modelling of complicated structures as they allow us to construct optimal order algebraic multilevel iterative solvers for a wide class of real-life elasticity problems. Copyright

A posteriori error estimates for subgrid viscosity stabilized approximations of convection–diffusion equations☆

Abstract We derive a posteriori error estimates for subgrid viscosity stabilized finite element approximations of convection–diffusion equations in the high Peclet number regime. Two estimators are analyzed: an asymptotically robust one and a fully robust one with respect to the Peclet number. Numerical results on test cases with boundary layers or internal layers show that the asymptotically robust estimator can be used to construct adaptive meshes.

A posteriori error analysis using the constitutive law for the Crouzeix–Raviart element☆

Abstract In this work, we study the error in the approximation of the solution of elliptic partial differential equations obtained with the nonconforming finite elements method; we adopt the error in a constitutive law approach.

Upper Bound of the Constant in Strengthened C.B.S. Inequality for Systems of Linear Partial Differential Equations

The constant γ in the strengthened Cauchy–Bunyakowski–Schwarz (C.B.S.) inequality plays a crucial role in the convergence rate of multilevel iterative methods as well as in the efficiency of a posteriori error estimators, that is the framework of finite element approximations of systems of partial differential equations. We consider an approximation of general systems of linear partial differential equations in R3. Concerning a multilevel convergence rate corresponding to nested general tetrahedral meshes of size h and 2h, we give an estimate of this constant for general three-dimensional cases.

Robust a posteriori error estimates for subgrid stabilization of non-stationary convection dominated diffusive transport

Abstract We derive a robust residual a posteriori error estimator for time-dependent convection–diffusion–reaction problem, stabilized by subgrid viscosity in space and discretized by Crank–Nicolson scheme in time. The estimator yields upper bounds on the error which are global in space and time and lower bounds that are global in space and local in time. Numerical experiments illustrate the theoretical performance of the error estimator.

On the Limiting Regularity Result of some Nonlinear Elliptic Equations

We shall prove the limiting regularity W 1, N(p−1) N−1 0 (Ω) of solutions of some nonlinear elliptic problems with right hand side in LLogL(Ω) and α ≥ N−1 N . Also, an improved regularity is given when α < N−1 N .

Option pricing under model involving slow growth volatility

In this paper, we present a new model of the European option price, it is about a model involving slow growth volatility. The SGV model (slow growth volatility model) is the name of the new model considered in this manuscript. The mathematical analysis shows that one has to resort to a degenerate parabolic equation, the resolution of which gives the price of the European option as a function of the time, the price of the underlying asset and the instantaneous volatility.

Parabolic inequalities in L1 as limits of renormalized equations

The paper deals with the existence of solutions of some parabolic bilateral problems approximated by the renormalized solutions of some parabolic equations.