Propagation of graphs in two-dimensional inhomogeneous media

被引：5
|
作者：
Deckelnick, Klaus
Elliott, Charles M.
机构：
[1] Univ Magdeburg, Inst Anal & Numer, D-39106 Magdeburg, Germany
[2] Univ Sussex, Dept Math, Brighton BN1 9RF, E Sussex, England
来源：
APPLIED NUMERICAL MATHEMATICS | 2006年 / 56卷 / 09期
关键词：
front propagation; Eikonal equation; viscosity solution; discontinuous Hamiltonian; striated medium; finite difference scheme; error bounds;
D O I：
10.1016/j.apnum.2006.03.009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the propagation of a front in a two-dimensional striated medium. In the case of a front that can be written as a graph over the real line we are led to an Eikonal equation for the height function which contains a possibly discontinuous coefficient. We prove existence and uniqueness of a viscosity solution in the sense of Ishii. Furthermore, we obtain an O(root h)-error bound for a monotone and consistent finite difference scheme. We conclude with some numerical tests. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.
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页码：1163 / 1178
页数：16
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