L∞ -error estimates of finite element methods with Euler time discretization scheme for an evolutionary HJB equations with nonlinear source terms

• Autorzy: Boulaaras S. , Bencheikh Le Hocine M. A. , Haiour M.

Identyfikatory

DOI

10.17512/jamcm.2017.1.02

• Języki publikacji: EN

Abstrakty

EN

The main purpose of this paper is to analyze the convergence of the proposed algorithm of the finite element methods coupled with a Euler discretization scheme. Also, an optimal error estimate with an asymptotic behavior in uniform norm are given for an evolutionary nonlinear Hamilton Jacobi Bellman (HJB) equation with respect to the Dirichlet boundary conditions.

Słowa kluczowe

EN

QVIs; finite elements; theta scheme fixed point; HJB equations; geometric convergence

PL

metody elementów skończonych; równanie Hamilton Jacobi Bellman; konwergencja geometryczna

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2017
• Tom: Vol. 16, nr 1
• Strony: 19--31
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Boulaaras S.

• Department of Mathematics, College of Science and Arts, Ar-Ras, Qassim University Kingdom of Saudi Arabia
• Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran 1 Ahmed Benbella, Algeria, phone [phone]

autor

Bencheikh Le Hocine M. A.

• Department of Mathematics, Faculty of Science, University of Annaba, Box. 12 Annaba 23000, Algeria
• Tamanghesset University Center, Box. 10034, Sersouf, Tamanghesset 11000, Algeria

autor

Haiour M.

• Department of Mathematics, Faculty of Science, University of Annaba, Box. 12 Annaba 23000, Algeria

Bibliografia

• [1] Boulaaras S., Haiour M., The finite element approximation of evolutionary Hamilton-Jacobi-Bellman equations with nonlinear source terms, Ind. Math. 2013, 24, 161-173.
• [2] Boulaaras S., Haiour M., The theta time scheme combined with a finite element spatial approximation of Hamilton-Jacobi-Bellman equation, Comput. Math. Model. 2014, 25, 423-438.
• [3] Cortey-Dumont P., On the finite element approximation in the L∞ -norm of variational inequalities with nonlinear operators, Numer. Math., 1985, 47, 45-57.
• [4] Bensoussan A., Lions J.L., Applications des inequations variationnelles en controle stochastique, Dunod, Paris 1978.
• [5] Cortey-Dumont P., Sur I’ analyse numerique des equations de Hamilton-Jacobi-Bellman, Math. Meth. in Appl. Sci. 1987.
• [6] Nitsche J., L∞ -convergence of finite element approximations, Mathematical aspects of finite element methods, Lect. Notes. Math. 1977, 606, 261-274.
• [7] Lions P.L., Mercier B., Approximation numérique des equations de Hamilton Jacobi Bellman, RAIRO, Anal. Num. 1980, 14, 369-393.
• [8] Boulbrachene M., Haiour M., The finite element approximation of Hamilton Jacobi Bellman equations, Comput. Math. Appl. 2001, 41, 993-1007.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).