Multiscale Modeling &Simulation, Volume 19, Issue 2, Page 1041-1065, January 2021.
In the first part of the paper, we propose and rigorously analyze a mixed finite element method for the approximation of the periodic strong solution to the fully nonlinear second-order Hamilton--Jacobi--Bellman equation with coefficients satisfying the Cordes condition. These problems arise as the corrector problems in the homogenization of Hamilton--Jacobi--Bellman equations. The second part of the paper focuses on the numerical homogenization of such equations, more precisely on the numerical approximation of the effective Hamiltonian. Numerical experiments demonstrate the approximation scheme for the effective Hamiltonian and the numerical solution of the homogenized problem.

中文翻译：

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周期 Hamilton--Jacobi--Bellman 问题的混合有限元逼近在数值均质化中的应用

多尺度建模与仿真，第 19 卷，第 2 期，第 1041-1065 页，2021
年1 月。在论文的第一部分，我们提出并严格分析了一种混合有限元方法，用于逼近完全非线性二次方程的周期性强解。使用满足 Cordes 条件的系数对 Hamilton--Jacobi--Bellman 方程进行排序。这些问题是作为 Hamilton--Jacobi--Bellman 方程均质化中的校正问题出现的。论文的第二部分侧重于此类方程的数值均匀化，更准确地说是有效哈密顿量的数值近似。数值实验证明了有效哈密顿量的近似方案和齐次化问题的数值解。