Numerical Solution for a Parabolic Obstacle Problem with Nonsmooth Initial Data

被引：8

作者：

Yang, Xiaozhong ^{[1
]}

Wang, Guanghui ^{[2
]}

Gu, Xiangqian ^{[2
]}

机构：

[1] North China Elect Power Univ, Sch Math & Phys, Beijing 102206, Peoples R China

[2] Chinese Acad Meteorol Sci, State Key Lab Severe Weather LaSW, Beijing 100081, Peoples R China

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2014年 / 30卷 / 05期

关键词：

error estimate; finite element method; numerical simulation; obstacle problem; regularization method; AMERICAN OPTION VALUATION; FINITE-VOLUME METHOD; VARIATIONAL INEQUALITY; UNILATERAL PROBLEMS; FREE-BOUNDARY; APPROXIMATION; CONVERGENCE;

D O I：

10.1002/num.21893

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article discusses the finite element approximation of solutions to a variational inequality of a parabolic obstacle problem with a nonsmooth initial data by a piecewise linear finite element discretization in space and an implicit time-stepping scheme. We show that the error of the approximation in a certain norm is of order O(h + Delta t(1/2)) by regularization method under some realistic regularity assumptions on the exact solution, where Delta t is the time step and h is the mesh parameter of the spatial partition. Numerical examples are presented to confirm our theoretical results. (c) 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1740-1754, 2014

引用

页码：1740 / 1754

页数：15

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