Elisabetta Carlini, Francisco J. Silva, Ahmad Zorkot
{"title":"A Lagrange–Galerkin Scheme for First Order Mean Field Game Systems","authors":"Elisabetta Carlini, Francisco J. Silva, Ahmad Zorkot","doi":"10.1137/23m1561762","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 167-198, February 2024. <br/> Abstract. In this work, we consider a first order mean field game system with nonlocal couplings. A Lagrange–Galerkin scheme for the continuity equation, coupled with a semi-Lagrangian scheme for the Hamilton–Jacobi–Bellman equation, is proposed to discretize the mean field games system. The convergence of solutions to the scheme towards a solution to the mean field game system is established in arbitrary space dimensions. The scheme is implemented to approximate two mean field games systems in dimensions one and two.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"7 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Numerical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1561762","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 167-198, February 2024. Abstract. In this work, we consider a first order mean field game system with nonlocal couplings. A Lagrange–Galerkin scheme for the continuity equation, coupled with a semi-Lagrangian scheme for the Hamilton–Jacobi–Bellman equation, is proposed to discretize the mean field games system. The convergence of solutions to the scheme towards a solution to the mean field game system is established in arbitrary space dimensions. The scheme is implemented to approximate two mean field games systems in dimensions one and two.
期刊介绍：
SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.
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