论文标题
汉密尔顿 - 雅各比 - 贝尔曼方程的梯度回收的最小二乘方法与电线系数
A least-squares Galerkin approach to gradient recovery for Hamilton-Jacobi-Bellman equation with Cordes coefficients
论文作者
论文摘要
我们提出了一种符合的有限元方法，以近似二阶汉密尔顿 - 雅各比 - 贝尔曼方程的强溶液，并具有差异的边界和满足电线条件的系数。我们显示了全线汉密尔顿 - 雅各比 - 贝尔曼方程的连续性半齿方法的融合。将此线性化适用于方程式，以非散发形式的线性椭圆边界值问题的递归序列。我们通过Lakkis＆Mousavi的最小二乘梯度回收[2021，arxiv：1909.00491]来处理这种BVP。我们为近似值提供了最佳速率APRIORI和aposteriori误差界限。 Aposteriori误差用于驱动自适应改进程序。我们通过对均匀和自适应网格进行计算机实验来调和理论发现。
We propose a conforming finite element method to approximate the strong solution of the second order Hamilton-Jacobi-Bellman equation with Dirichlet boundary and coefficients satisfying Cordes condition. We show the convergence of the continuum semismooth Newton method for the fully nonlinear Hamilton-Jacobi-Bellman equation. Applying this linearization for the equation yields a recursive sequence of linear elliptic boundary value problems in nondivergence form. We deal numerically with such BVPs via the least-squares gradient recovery of Lakkis & Mousavi [2021, arxiv:1909.00491]. We provide an optimal-rate apriori and aposteriori error bounds for the approximation. The aposteriori error are used to drive an adaptive refinement procedure. We close with computer experiments on uniform and adaptive meshes to reconcile the theoretical findings.
