L1-APPROXIMATION OF STATIONARY HAMILTON-JACOBI EQUATIONS

被引：10
|
作者：
Guermond, Jean-Luc [1 ]
Popov, Bojan [1 ]
机构：
[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2008年 / 47卷 / 01期
基金：
美国国家科学基金会;
关键词：
finite elements; best L-1-approximation; viscosity solution; Hamilton-Jacobi equations;
D O I：
10.1137/070681922
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We describe a nonlinear finite element technique to approximate the solutions of stationary Hamilton-Jacobi equations in two space dimensions using continuous finite elements of arbitrary degree. The method consists of minimizing a functional containing the L-1-norm of the Hamiltonian plus a discrete entropy. It is shown that the approximate sequence converges to the unique viscosity solution under appropriate hypotheses on the Hamiltonian and the mesh family.
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页码：339 / 362
页数：24
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