Rates of convergence of finite element approximations of second-order mean field games with nondifferentiable Hamiltonians
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908898538029056 |
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| author | Osborne, Yohance A. P. Smears, Iain |
| author_facet | Osborne, Yohance A. P. Smears, Iain |
| contents | We prove a rate of convergence for finite element approximations of stationary, second-order mean field games with nondifferentiable Hamiltonians posed in general bounded polytopal Lipschitz domains with strongly monotone running costs. In particular, we obtain a rate of convergence in the $H^1$-norm for the value function approximations and in the $L^2$-norm for the approximations of the density. We also establish a rate of convergence for the error between the exact solution of the MFG system with a nondifferentiable Hamiltonian and the finite element discretizations of the corresponding MFG system with a regularized Hamiltonian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rates of convergence of finite element approximations of second-order mean field games with nondifferentiable Hamiltonians Osborne, Yohance A. P. Smears, Iain Numerical Analysis 65N15, 65N30, 35Q89 We prove a rate of convergence for finite element approximations of stationary, second-order mean field games with nondifferentiable Hamiltonians posed in general bounded polytopal Lipschitz domains with strongly monotone running costs. In particular, we obtain a rate of convergence in the $H^1$-norm for the value function approximations and in the $L^2$-norm for the approximations of the density. We also establish a rate of convergence for the error between the exact solution of the MFG system with a nondifferentiable Hamiltonian and the finite element discretizations of the corresponding MFG system with a regularized Hamiltonian. |
| title | Rates of convergence of finite element approximations of second-order mean field games with nondifferentiable Hamiltonians |
| topic | Numerical Analysis 65N15, 65N30, 35Q89 |
| url | https://arxiv.org/abs/2506.03039 |