Volume 56, Number 2, March-April 2022
|Page(s)||679 - 704|
|Published online||15 March 2022|
Discontinuous Galerkin and C0-IP finite element approximation of periodic Hamilton–Jacobi–Bellman–Isaacs problems with application to numerical homogenization
Haas F1 Team, Vehicle Sciences, Overthorpe Rd, Banbury OX16 4PN, UK
2 Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076, Singapore
* Corresponding author: email@example.com
Accepted: 9 February 2022
In the first part of the paper, we study the discontinuous Galerkin (DG) and C0 interior penalty (C0-IP) finite element approximation of the periodic strong solution to the fully nonlinear second-order Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation with coefficients satisfying the Cordes condition. We prove well-posedness and perform abstract a posteriori and a priori analyses which apply to a wide family of numerical schemes. These periodic problems arise as the corrector problems in the homogenization of HJBI equations. The second part of the paper focuses on the numerical approximation to the effective Hamiltonian of ergodic HJBI operators via DG/C0-IP finite element approximations to approximate corrector problems. Finally, we provide numerical experiments demonstrating the performance of the numerical schemes.
Mathematics Subject Classification: 35B27 / 35J60 / 65N12 / 65N15 / 65N30
Key words: Hamilton–Jacobi–Bellman and HJB–Isaacs equations / nondivergence-form elliptic PDE / Cordes condition / nonconforming finite element methods / homogenization
© The authors. Published by EDP Sciences, SMAI 2022
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