Error estimates of finite element methods for nonlinear fractional stochastic differential equations
Abstract In this paper, we consider the Galerkin finite element approximations of the initial value problem for the nonlinear fractional stochastic partial differential equations with multiplicative noise. We study a spatial semidiscrete scheme with the standard Galerkin finite element method and a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-06-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1665-0 |
| _version_ | 1819161165832388608 |
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| author | Yanpeng Zhang Xiaoyuan Yang Xiaocui Li |
| author_facet | Yanpeng Zhang Xiaoyuan Yang Xiaocui Li |
| author_sort | Yanpeng Zhang |
| collection | DOAJ |
| description | Abstract In this paper, we consider the Galerkin finite element approximations of the initial value problem for the nonlinear fractional stochastic partial differential equations with multiplicative noise. We study a spatial semidiscrete scheme with the standard Galerkin finite element method and a fully discrete scheme based on the Goreno–Mainardi–Moretti–Paradisi (GMMP) scheme. We establish strong convergence error estimates for both semidiscrete and fully discrete schemes. |
| first_indexed | 2024-12-22T17:08:01Z |
| format | Article |
| id | doaj.art-4b17e32fd9744b53ab263fbffbd76dcc |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-22T17:08:01Z |
| publishDate | 2018-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-4b17e32fd9744b53ab263fbffbd76dcc2022-12-21T18:19:09ZengSpringerOpenAdvances in Difference Equations1687-18472018-06-012018112010.1186/s13662-018-1665-0Error estimates of finite element methods for nonlinear fractional stochastic differential equationsYanpeng Zhang0Xiaoyuan Yang1Xiaocui Li2LMIB and School of Mathematics and Systems Science, Beihang UniversityLMIB and School of Mathematics and Systems Science, Beihang UniversitySchool of Science, Beijing University of Chemical TechnologyAbstract In this paper, we consider the Galerkin finite element approximations of the initial value problem for the nonlinear fractional stochastic partial differential equations with multiplicative noise. We study a spatial semidiscrete scheme with the standard Galerkin finite element method and a fully discrete scheme based on the Goreno–Mainardi–Moretti–Paradisi (GMMP) scheme. We establish strong convergence error estimates for both semidiscrete and fully discrete schemes.http://link.springer.com/article/10.1186/s13662-018-1665-0Nonlinear fractional stochastic differential equationsFinite element methodError estimatesStrong convergenceInitial value problem |
| spellingShingle | Yanpeng Zhang Xiaoyuan Yang Xiaocui Li Error estimates of finite element methods for nonlinear fractional stochastic differential equations Advances in Difference Equations Nonlinear fractional stochastic differential equations Finite element method Error estimates Strong convergence Initial value problem |
| title | Error estimates of finite element methods for nonlinear fractional stochastic differential equations |
| title_full | Error estimates of finite element methods for nonlinear fractional stochastic differential equations |
| title_fullStr | Error estimates of finite element methods for nonlinear fractional stochastic differential equations |
| title_full_unstemmed | Error estimates of finite element methods for nonlinear fractional stochastic differential equations |
| title_short | Error estimates of finite element methods for nonlinear fractional stochastic differential equations |
| title_sort | error estimates of finite element methods for nonlinear fractional stochastic differential equations |
| topic | Nonlinear fractional stochastic differential equations Finite element method Error estimates Strong convergence Initial value problem |
| url | http://link.springer.com/article/10.1186/s13662-018-1665-0 |
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