论文标题
周期性汉密尔顿的混合有限元近似 - 雅各比 - 贝尔曼在数值均质化中的应用问题
Mixed finite element approximation of periodic Hamilton--Jacobi--Bellman problems with application to numerical homogenization
论文作者
论文摘要
在本文的第一部分中，我们提出并严格分析一种混合有限元方法，以将周期性强溶液近似于完全非线性的二阶汉密尔顿 - 雅各比 - 贝尔曼方程，其系数满足了绳索条件。这些问题是汉密尔顿 - 雅各比 - 贝尔曼方程的均质问题的纠正问题。本文的第二部分重点介绍了此类方程的数值均匀化，更准确地说是有效的哈密顿量的数值近似。数值实验证明了有效的哈密顿量和同质性问题的数值解决方案的近似方案。
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.
