| Title | OPTIMAL ANALYSIS OF FINITE ELEMENT METHODS FOR THE STOCHASTIC STOKES EQUATIONS |
| Creator | |
| Date Issued | 2025-03-01 |
| Source Publication | Mathematics of Computation
 |
| ISSN | 0025-5718 |
| Volume | 94Issue:352Pages:551-583 |
| Abstract | Numerical analysis for the stochastic Stokes equations is still challenging even though it has been well done for the corresponding deterministic equations. In particular, the pre-existing error estimates of finite element methods for the stochastic Stokes equations in the L∞(0, T; L(Ω; L)) norm all suffer from the order reduction with respect to the spatial discretizations. The best convergence result obtained for these fully discrete schemes is only half-order in time and first-order in space, which is not optimal in space in the traditional sense. The objective of this article is to establish strong convergence of O(τ + h) in the L∞(0, T; L(Ω; L)) norm for approximating the velocity, and strong convergence of O(τ 1/2 +h) in the L∞(0, T; L(Ω; L)) norm for approximating the time integral of pressure, where τ and h denote the temporal step size and spatial mesh size, respectively. The error estimates are of optimal order for the spatial discretization considered in this article (with MINI element), and consistent with the numerical experiments. The analysis is based on the fully discrete Stokes semigroup technique and the corresponding new estimates. |
| Keyword | analytic semigroup error estimate mixed FEM multiplicative noise semi-implicit Euler scheme Stochastic Stokes equation Wiener process |
| DOI | 10.1090/mcom/3972 |
| URL | View source |
| Language | 英语English |
| Scopus ID | 2-s2.0-85213007384 |
| Citation statistics | |
| Document Type | Journal article |
| Identifier | http://repository.uic.edu.cn/handle/39GCC9TT/12501 |
| Collection | Beijing Normal-Hong Kong Baptist University |
| Corresponding Author | Sun，Weiwei |
| Affiliation | 1.Department of Applied Mathematics,The Hong Kong Polytechnic University,Hong Kong 2.Department of Mathematics,National University of Singapore,Singapore,119076,Singapore 3.Research Center for Mathematics,Beijing Normal University,Zhuhai,China 4.Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science,BNU-HKBU United International College,Zhuhai,China |
| Corresponding Author Affilication | Beijing Normal-Hong Kong Baptist University |
| Recommended Citation GB/T 7714 | Li，Buyang,Ma，Shu,Sun，Weiwei. OPTIMAL ANALYSIS OF FINITE ELEMENT METHODS FOR THE STOCHASTIC STOKES EQUATIONS[J]. Mathematics of Computation, 2025, 94(352): 551-583. |
| APA | Li，Buyang, Ma，Shu, & Sun，Weiwei. (2025). OPTIMAL ANALYSIS OF FINITE ELEMENT METHODS FOR THE STOCHASTIC STOKES EQUATIONS. Mathematics of Computation, 94(352), 551-583. |
| MLA | Li，Buyang,et al."OPTIMAL ANALYSIS OF FINITE ELEMENT METHODS FOR THE STOCHASTIC STOKES EQUATIONS". Mathematics of Computation 94.352(2025): 551-583. |
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