We propose a new semi-Lagrangian scheme for the game ∞-Laplacian. We demonstrate the convergence of the scheme to the viscosity solution of the given problem, showing its consistency, monotonicity, and stability. The proof of this result is established following the Barles-Souganidis analysis. This analysis assumes convergence at the boundary in a strong sense and is applied to our proposed scheme, augmented with an artificial viscosity term.
A Convergent Semi-Lagrangian Scheme for the Game ∞-Laplacian / Carlini, E.; Tozza, S.. - In: DYNAMIC GAMES AND APPLICATIONS. - ISSN 2153-0785. - (2024). [10.1007/s13235-024-00596-1]
A Convergent Semi-Lagrangian Scheme for the Game ∞-Laplacian
Carlini E.
;
2024
Abstract
We propose a new semi-Lagrangian scheme for the game ∞-Laplacian. We demonstrate the convergence of the scheme to the viscosity solution of the given problem, showing its consistency, monotonicity, and stability. The proof of this result is established following the Barles-Souganidis analysis. This analysis assumes convergence at the boundary in a strong sense and is applied to our proposed scheme, augmented with an artificial viscosity term.| File | Dimensione | Formato | |
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