Multilevel Monte Carlo front-tracking for random scalar conservation laws

被引：9

作者：

Risebro, Nils Henrik ^{[1
]}

Schwab, Christoph ^{[2
]}

Weber, Franziska ^{[1
]}

机构：

[1] Univ Oslo, Dept Math, POB 1053, N-0316 Oslo, Norway

[2] ETH, ETH Zentrum HG G 57 1, Seminar Appl Math, Ramistr 101, Zurich, Switzerland

来源：

BIT NUMERICAL MATHEMATICS | 2016年 / 56卷 / 01期

关键词：

Conservation laws; Random flux; Front tracking; Monte Carlo method; FINITE-VOLUME METHODS; BURGERS-EQUATION; SYSTEMS;

D O I：

10.1007/s10543-015-0550-4

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We consider random scalar hyperbolic conservation laws in spatial dimension with bounded random flux functions which are Lipschitz continuous with respect to the state variable, for which there exists a unique random entropy solution. We present a convergence analysis of a multilevel Monte Carlo front-tracking algorithm. It is based on "pathwise" application of the front-tracking method for deterministic conservation laws. Due to the first order convergence of front tracking, we obtain an improved complexity estimate in one space dimension.

引用

页码：263 / 292

页数：30

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