{"title":"Recovery Based Linear Finite Element Methods for Hamilton–Jacobi–Bellman Equation with Cordes Coefficients","authors":"Tianyang Chu, Hailong Guo, Zhimin Zhang","doi":"10.1137/23m1579297","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 1, Page 23-53, February 2025. <br/> Abstract. In this paper, we design a simple and convergent [math] linear finite element method for the linear second-order elliptic equation in nondivergence form and extend it to the Hamilton–Jacobi–Bellman equation. Motivated by the Miranda–Talenti estimate, we establish a discrete analogue of the estimate for the [math] linear finite element space based on a new gradient recovery operator. The construction and properties of the gradient recovery operator, including its superconvergent property on mildly structured meshes, are discussed. We provide a proof of convergence for the proposed methods and support the theory with numerical experiments.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"27 1","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2025-01-06","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/10.1137/23m1579297","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Numerical Analysis, Volume 63, Issue 1, Page 23-53, February 2025. Abstract. In this paper, we design a simple and convergent [math] linear finite element method for the linear second-order elliptic equation in nondivergence form and extend it to the Hamilton–Jacobi–Bellman equation. Motivated by the Miranda–Talenti estimate, we establish a discrete analogue of the estimate for the [math] linear finite element space based on a new gradient recovery operator. The construction and properties of the gradient recovery operator, including its superconvergent property on mildly structured meshes, are discussed. We provide a proof of convergence for the proposed methods and support the theory with numerical experiments.
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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