L ∞-error estimates of a finite element method for Hamilton-Jacobi-Bellman equations with nonlinear source terms with mixed boundary condition

• Autorzy: Miloudi Madjda , Saadi Samira , Haiour Mohamed

Identyfikatory

DOI

10.1515/dema-2021-0043

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

algorithm; contraction; finite element; fixed point; Hamilton-Jacobi-Bellman equation; L ∞-error estimate

PL

algorytm; kontrakcja; element skończony; punkt stały; równanie Hamiltona-Jacobiego-Bellmana; szacowanie błędu

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 452--461
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Miloudi Madjda

• Department of Mathematics, University Badji Mokhtar Annaba, Box. 12, Annaba 23000, Algeria

autor

Saadi Samira

• Department of Mathematics, University Badji Mokhtar Annaba, Box. 12, Annaba 23000, Algeria

autor

Haiour Mohamed

• Department of Mathematics, University Badji Mokhtar Annaba, Box. 12, Annaba 23000, Algeria

Bibliografia

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• [9] S. Boulaaras and M. Haiour, L∞-asymptotic behavior for a finite element approximation in parabolic quasi-variational inequalities related to impulse control problem, Appl. Math. Comput. 217 (2011), 6443–6450.
• [10] S. Boulaaras and M. Haiour, A general case for the maximum norm analysis of an overlapping Schwarz methods of evolutionary HJB equation with nonlinear source terms with the mixed boundary conditions, Appl. Math. Inf. Sci. 9 (2015), no. 3, 18.
• [11] M. Boulbrachene, L∞-error estimates of a finite element method for the Hamilton Jacobi Bellman equations, Int. Cent. Theor. Phys. 1 (1995), 1–8.
• [12] J. Nitsche, L∞-convergence of finite element approximations, Mathematical aspects of finite element methods, Lect. Notes Math. 606 (1977), 261–274.
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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).