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2 results on '"fixed point hamilton-jacobi-bellman equation"'

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

Author

Miloudi Madjda, Saadi Samira, and Haiour Mohamed

Subjects
algorithm, contraction, finite element, fixed point hamilton-jacobi-bellman equation, l∞-error estimate, 65f30, 47h09, 65l60, 47h10, 60h15, 65m12, Mathematics, QA1-939
Abstract

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.

Published
2021
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2. L∞-error estimates of a finite element method for Hamilton-Jacobi-Bellman equations with nonlinear source terms with mixed boundary condition

Author

Madjda Miloudi, Samira Saadi, and Mohamed Haiour

Subjects
47h09, algorithm, General Mathematics, fixed point hamilton-jacobi-bellman equation, 65m12, contraction, finite element, 60h15, QA1-939, l∞-error estimate, 65f30, 65l60, 47h10, Mathematics
Abstract

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.

Published
2021

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