ON THE CONVERGENCE OF FINITE ELEMENT METHODS FOR HAMILTON-JACOBI-BELLMAN EQUATIONS

被引：52

作者：

Jensen, Max ^{[1
]}

Smears, Iain ^{[2
]}

机构：

[1] Univ Durham, Dept Math Sci, Durham DH1 3LE, England

[2] Univ Oxford, Inst Math, Oxford OX1 3LB, England

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2013年 / 51卷 / 01期

关键词：

finite element methods; partial differential equations; Hamilton-Jacobi-Bellman equations; viscosity solutions; DISCRETE MAXIMUM PRINCIPLE; DIFFERENCE APPROXIMATIONS; PARABOLIC EQUATIONS; VISCOSITY SOLUTIONS; DIFFUSION; SCHEMES;

D O I：

10.1137/110856198

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the convergence of monotone P1 finite element methods on unstructured meshes for fully nonlinear Hamilton-Jacobi-Bellman equations arising from stochastic optimal control problems with possibly degenerate, isotropic diffusions. Using elliptic projection operators we treat discretizations which violate the consistency conditions of the framework by Barles and Souganidis. We obtain strong uniform convergence of the numerical solutions and, under nondegeneracy assumptions, strong L-2 convergence of the gradients.

引用

页码：137 / 162

页数：26

共 38 条

[1]

[Anonymous], 2006, SPRINGER SER COMPUT

[2]

Barles G., 1991, Asymptotic Analysis, V4, P271

[3] EXIT TIME PROBLEMS IN OPTIMAL-CONTROL AND VANISHING VISCOSITY METHOD [J].