Numerical solution for a parabolic obstacle problem with nonsmooth initial data | Zendy

Yang Xiaozhong | Zendy; Wang Guanghui | Zendy; Gu Xiangqian | Zendy

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Numerical solution for a parabolic obstacle problem with nonsmooth initial data

Author(s) -

Yang Xiaozhong,

Wang Guanghui,

Gu Xiangqian

Publication year - 2014

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.21893

Subject(s) - mathematics , discretization , variational inequality , obstacle problem , finite element method , piecewise , partial differential equation , piecewise linear function , norm (philosophy) , mathematical analysis , regularization (linguistics) , partition of unity , numerical analysis , physics , artificial intelligence , political science , computer science , law , thermodynamics

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 + Δ t 1 / 2 ) by regularization method under some realistic regularity assumptions on the exact solution, where Δ t is the time step and h is the mesh parameter of the spatial partition. Numerical examples are presented to confirm our theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1740–1754, 2014

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