Discontinuous Galerkin finite element methods for time-dependent Hamilton–Jacobi–Bellman equations with Cordes coefficients
Discontinuous Galerkin finite element methods for time-dependent Hamilton–Jacobi–Bellman equations with Cordes coefficients
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DOI：
10.1007/s00211-015-0741-6
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发表时间：
2014-06
影响因子：
2.1
通讯作者：
Iain Smears;E. Süli
中科院分区：
文献类型：
--
作者：
Iain Smears;E. Süli
本文提出并分析了一种求解带Cordes系数的抛物型Hamilton-Jacobi-Bellman方程的全离散间断Galerkin时间步方法。该方法在一般的非结构网格和时间划分上是一致的和无条件稳定的。粗糙和定期解决方案的时间规律性方面的误差界表明，该方法是任意高阶的最佳收敛速度的网格大小，时间间隔长度和时间多项式的程度，并可能次优的顺序和半的空间多项式的程度。强各向异性扩散系数和早期奇异性问题的数值实验表明，该方法的准确性和计算效率，与指数收敛速度下combinedhp和细化。
We propose and analyse a fully discrete discontinuous Galerkin time-stepping method for parabolic Hamilton–Jacobi–Bellman equations with Cordes coefficients. The method is consistent and unconditionally stable on rather general unstructured meshes and time-partitions. Error bounds for both rough and regular solutions in terms of temporal regularity show that the method is arbitrarily high-order with optimal convergence rates with respect to the mesh size, time-interval length and temporal polynomial degree, and possibly suboptimal by an order and a half in the spatial polynomial degree. Numerical experiments on problems with strongly anisotropic diffusion coefficients and early-time singularities demonstrate the accuracy and computational efficiency of the method, with exponential convergence rates achieved under combinedhp- and-refinement.