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In this paper, we introduce a new method to analyze the convergence of the standard finite element method for Hamilton-Jacobi-Bellman equation with noncoercive operators with nonlinear source terms with the mixed boundary conditions. The method consists of combining Bensoussan-Lions algorithm with the characterization of the solution, in both the continuous and discrete contexts, as fixed point of contraction. Optimal error estimates are then derived, first between the continuous algorithm and its finite element counterpart and then between the continuous solution and the approximate solution.

This study aims to investigate numerically and theoretically a thermoelastic Bresse system where the heat conduction given by the Green and Naghdi theories. Theoretically, we establish the existence and uniqueness of solutions as well as the exponential stability regardless of the system's parameters. Numerically, we present a finite element approximation, and we show the discrete energy decay. At the end, we provide some numerical results with an error estimate based on additional regularity of the solution. [ABSTRACT FROM AUTHOR]

The paper studies the existence result for a new class of Kirchhoff elliptic system with variable parameters in the right hand side. Sub-super solutions method are used for proving the main result. Our study is a natural improvement result of our previous one in (Boulaaras et al. in Math. Methods Appl. Sci. 41:5203-5210, 2018). [ABSTRACT FROM AUTHOR]

Motivated by the idea which has been introduced by Haiour and Boulaaras' work in [11], we provide a maximum norm analysis of a theta scheme combined with finite element Schwarz alternating method for a class of parabolic equation on two overlapping subdomains with nonmatching grids. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a stability analysis on the theta scheme which given by our work in [4], we establish, on each subdomain, an optimal asymptotic behavior between the discrete Schwarz sequence and the asymptotic solution of parabolic differential equations. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to analyze the convergence and regularity of our proposed algorithm of the finite element methods coupled with a theta time discretization scheme for evolutionary Hamilton-Jacobi-Bellman equations with linear source terms with respect to the Dirichlet boundary conditions (Appl. Math. Comput., 262 (2015), 42.55 ). Also, an optimal error estimate with an asymptotic behavior in uniform norm is given. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical analysis of the problem of parabolic quasi-variational inequalities related to impulse control problems. An optimal L -convergence of a piecewise linear finite element method is established using the concept of subsolution. [ABSTRACT FROM AUTHOR]

In this article, an optimal error estimate for parabolic variational inequalities is studied. Existence and uniqueness of the solution is provided by the introduction of a constructive algorithm. An optimallyL∞-asymptotic behavior in uniform norm is proved using the semi-implicit time scheme combined with the finite element spatial approximation. The approach is based on the concept of subsolutions. [ABSTRACT FROM PUBLISHER]

Abstract: This paper is an extension for our previous results [3–5], and it deals with the finite element approximation of a parabolic quasi-variational inequalities with mixed boundary conditions. A quasi-optimal L ∞-error estimate is established using a new discrete algorithm stands in theta time scheme combined with a finite element spatial approximation. Our approach stands on a discrete L ∞-stability property with respect to the right-hand side where the obstacle defined as an impulse control problem. [Copyright &y& Elsevier]

Abstract: In this paper, the parabolic quasi-variational inequalities are transformed into a noncoercive elliptic quasi-variational inequalities. A new iterative discrete algorithm is proposed to show the existence and uniqueness, and a simple proof to asymptotic behavior in uniform norm is also given using the theta time scheme combined with a finite element spatial approximation. The proposed approach stands on a discrete L ∞-stability property with respect to the right-hand side and obstacle defined as an impulse control problem. [Copyright &y& Elsevier]

The paper deals with the theta time scheme combined with a finite element spatial approximation of parabolic variational inequalities. The parabolic variational inequalities are transformed into noncoercive elliptic variational inequalities. A simple result to time energy behavior is proved, and a new iterative discrete algorithm is proposed to show the existence and uniqueness. Moreover, its convergence is established. Furthermore, a simple proof to asymptotic behavior in uniform norm is given. [ABSTRACT FROM AUTHOR]

In the context of the development of the research project (Boulaaras et al.) which was supported by the Deanship of Scientific Research of Qassim University under the Project No. 1140 during the academic year 2016/1437, this research will introduce a two dimensional mathematical model based on the finite elements spatial method combined with a finite differences time scheme applied to the diffusion equations. This model will be applied in the hypothetical example where the obtained results will be compared with the real experimental data. Such a comparison will allow to predict the soil temperature for different depths and at different time periods according to certain conditions on the weather and take into account the stability conditions of the used numerical method. It's worthy of note that some of the concreted mathematical problems will be addressed by the experimental scientific theories of functional analysis and then the numerical simulation of the theoretical study will be provided thanks to sophisticated methods with more convergence and stability. This mathematical model would be reduced by means of physical measurement and also in charge of the physical cost. [ABSTRACT FROM AUTHOR]

Abstract A finite element method and implicit time steps are used to determine the price of an American option. The algorithm of Brennan and Schwartz is adapted to this situation and we prove convergence. Numerical tests confirm the theoretical result and lead to a smaller error for the same computational effort, compared to the finite difference method. [ABSTRACT FROM AUTHOR]

In this paper, an optimal error estimate for system of parabolic quasi-variational inequalities related to stochastic control problems is studied. Existence and uniqueness of the solution is provided by the introduction of a constructive algorithm. An optimally L∞-asymptotic behavior in maximum norm is proved using the semiimplicit time scheme combined with the finite element spatial approximation. The approach is based on the concept of subsolution and discrete regularity. [ABSTRACT FROM AUTHOR]