Well-Posedness and Finite Element Approximations for Elliptic SPDEs with Gaussian Noises
文献类型：期刊论文
| 作者 | Yanzhao Cao1; Jialin Hong2; Zhihui Liu3 |
| 刊名 | 数学研究通讯:英文版
 |
| 出版日期 | 2020 |
| 卷号 | 36.0期号:002页码:113-127 |
| 关键词 | Elliptic stochastic partial differential equation spectral approximations finite element approximations power-law noise |
| ISSN号 | 1674-5647 |
| 其他题名 | Well-posedness and Finite Element Approximations for Elliptic SPDEs with Gaussian Noises |
| 英文摘要 | The paper studies the well-posedness and optimal error estimates of spectral finite element approximations for the boundary value problems of semi-linear elliptic SPDEs driven by white or colored Gaussian noises.The noise term is approximated through the spectral projection of the covariance operator,which is not required to be commutative with the Laplacian operator.Through the convergence analysis of SPDEs with the noise terms replaced by the projected noises,the well-posedness of the SPDE is established under certain covariance operator-dependent conditions.These SPDEs with projected noises are then numerically approximated with the finite element method.A general error estimate framework is established for the finite element approximations.Based on this framework,optimal error estimates of finite element approximations for elliptic SPDEs driven by power-law noises are obtained.It is shown that with the proposed approach,convergence order of white noise driven SPDEs is improved by half for one-dimensional problems,and by an infinitesimal factor for higher-dimensional problems. |
| 语种 | 中文 |
| CSCD记录号 | CSCD:6768199 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/57702]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 作者单位 | 1.Department of Mathematics,Auburn University,Auburn,USA 2.中国科学院数学与系统科学研究院 3.Department of Mathematics,The Hong Kong University of Science and Technology,Hong Kong SAR |
| 推荐引用方式 GB/T 7714 | Yanzhao Cao,Jialin Hong,Zhihui Liu. Well-Posedness and Finite Element Approximations for Elliptic SPDEs with Gaussian Noises[J]. 数学研究通讯:英文版,2020,36.0(002):113-127. |
| APA | Yanzhao Cao,Jialin Hong,&Zhihui Liu.(2020).Well-Posedness and Finite Element Approximations for Elliptic SPDEs with Gaussian Noises.数学研究通讯:英文版,36.0(002),113-127. |
| MLA | Yanzhao Cao,et al."Well-Posedness and Finite Element Approximations for Elliptic SPDEs with Gaussian Noises".数学研究通讯:英文版 36.0.002(2020):113-127. |
入库方式： OAI收割
来源：数学与系统科学研究院
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