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Equal Lower-order Finite Elements of Least-squares Type in Biot Poroelasticity Modeling 生物孔隙弹性模型中最小二乘型等低阶有限元
4区 数学
Taiwanese Journal of Mathematics Pub Date : 2023-09-20 DOI: 10.11650/tjm/230702
Hsueh-Chen Lee, Hyesuk Lee
{"title":"Equal Lower-order Finite Elements of Least-squares Type in Biot Poroelasticity Modeling","authors":"Hsueh-Chen Lee, Hyesuk Lee","doi":"10.11650/tjm/230702","DOIUrl":"https://doi.org/10.11650/tjm/230702","url":null,"abstract":"We investigate the behavior of the approximate solution of Biot's consolidation model using a weighted least-squares (WLS) finite element method. The model describes the fluid flow in a deformable porous medium, with variables for fluid pressure, velocity, and displacement. The WLS functional is defined based on the stress-displacement formulation, with the symmetry condition of the stress and the weight that depends on the time step size for the temporal discretization of the model. An a priori error estimate for the first-order linearized least squares (LS) system is analyzed, and its validity is confirmed through numerical results. By using continuous piecewise linear finite element spaces for all variables and adjusting the weight appropriately, we obtain optimal error convergence rates for all variables. Additionally, we present two numerical examples to demonstrate the implementation of the WLS method for benchmark problems.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136263541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Composition Operators on Hilbert Spaces of Dirichlet Series Dirichlet级数Hilbert空间上的复合算子
4区 数学
Taiwanese Journal of Mathematics Pub Date : 2023-03-20 DOI: 10.11650/tjm/220905
Maofa Wang, Min He
{"title":"Composition Operators on Hilbert Spaces of Dirichlet Series","authors":"Maofa Wang, Min He","doi":"10.11650/tjm/220905","DOIUrl":"https://doi.org/10.11650/tjm/220905","url":null,"abstract":"Motivated by a theorem of Gordon and Hedenmalm in 1999, the study of composition operators acting on various scales of function spaces of Dirchlet series has arisen intensive interest. In this paper, we characterize the boundedness of composition operators induced by specific Dirichlet series symbols from Bergman space to Hardy space of Dirichlet series.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135035407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Fractional-order Quasi-reversibility Method to a Backward Problem for the Multi-term Time-fractional Diffusion Equation 多项时间分数扩散方程逆向问题的分数阶拟可逆性方法
IF 0.4 4区 数学
Taiwanese Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.11650/tjm/230801
Liangliang Sun, Yuxin Wang, Maoli Chang
{"title":"A Fractional-order Quasi-reversibility Method to a Backward Problem for the Multi-term Time-fractional Diffusion Equation","authors":"Liangliang Sun, Yuxin Wang, Maoli Chang","doi":"10.11650/tjm/230801","DOIUrl":"https://doi.org/10.11650/tjm/230801","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42407445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Endpoint Sobolev Regularity of Multilinear Maximal Operators 多线性极大算子的端点Sobolev正则性
IF 0.4 4区 数学
Taiwanese Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.11650/tjm/230703
Feng Liu, Xiao Zhang, Huiyun Zhang
{"title":"Endpoint Sobolev Regularity of Multilinear Maximal Operators","authors":"Feng Liu, Xiao Zhang, Huiyun Zhang","doi":"10.11650/tjm/230703","DOIUrl":"https://doi.org/10.11650/tjm/230703","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46132730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Computing Algorithms in Resonant Regime for a Two-phase Flow Model 两相流模型共振区计算算法
4区 数学
Taiwanese Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.11650/tjm/230901
Dao Huy Cuong, Mai Duc Thanh
{"title":"Computing Algorithms in Resonant Regime for a Two-phase Flow Model","authors":"Dao Huy Cuong, Mai Duc Thanh","doi":"10.11650/tjm/230901","DOIUrl":"https://doi.org/10.11650/tjm/230901","url":null,"abstract":"Resonant regime in two-phase flow models causes tough problems for constructing computational Riemann solvers. The nonlinear algebraic equations that determine the states could be in implicit form. In this work, we develop computational algorithms for the states in Riemann solvers, which include a method of pattern search of the intersection points of composite wave curves associated with different characteristic fields. Numerical tests show that numerical schemes employing these algorithms provides us with a good accuracy. The schemes are also shown to be well-balanced in subsonic regions.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135550015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Limiting Spectral Distributions of Stochastic Block Models 随机块模型的极限谱分布
4区 数学
Taiwanese Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.11650/tjm/231004
May-Ru Chen, Giap Van Su
{"title":"On the Limiting Spectral Distributions of Stochastic Block Models","authors":"May-Ru Chen, Giap Van Su","doi":"10.11650/tjm/231004","DOIUrl":"https://doi.org/10.11650/tjm/231004","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135312898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Three-term Conjugate Gradient Method with a Random Parameter for Large-scale Unconstrained Optimization and its Application in Regression Model 大规模无约束优化的三项随机参数共轭梯度法及其在回归模型中的应用
IF 0.4 4区 数学
Taiwanese Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.11650/tjm/230503
Yueting Yang, Xue Zhang, Guoling Zhou, Mingyuan Cao
{"title":"A Three-term Conjugate Gradient Method with a Random Parameter for Large-scale Unconstrained Optimization and its Application in Regression Model","authors":"Yueting Yang, Xue Zhang, Guoling Zhou, Mingyuan Cao","doi":"10.11650/tjm/230503","DOIUrl":"https://doi.org/10.11650/tjm/230503","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48125634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Error Analysis of Nonconforming Virtual Element Method for Stokes Problem with Low Regularity 低正则性Stokes问题的非协调虚拟单元法的误差分析
IF 0.4 4区 数学
Taiwanese Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.11650/tjm/230205
Tonglin Wang, Jikun Zhao
{"title":"Error Analysis of Nonconforming Virtual Element Method for Stokes Problem with Low Regularity","authors":"Tonglin Wang, Jikun Zhao","doi":"10.11650/tjm/230205","DOIUrl":"https://doi.org/10.11650/tjm/230205","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47660476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Singular Limit Solutions for a $4$-dimensional Emden–Fowler System of Liouville Type in Some General Case 一般情况下$4$维Liouville型Emden-Fowler系统的奇异极限解
IF 0.4 4区 数学
Taiwanese Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.11650/tjm/221202
Lilia Larbi, N. Trabelsi
{"title":"Singular Limit Solutions for a $4$-dimensional Emden–Fowler System of Liouville Type in Some General Case","authors":"Lilia Larbi, N. Trabelsi","doi":"10.11650/tjm/221202","DOIUrl":"https://doi.org/10.11650/tjm/221202","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41755212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Orlicz–Hardy Weak Martingale Spaces for Two-parameter 两参数的Orlicz–Hardy弱鞅空间
IF 0.4 4区 数学
Taiwanese Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.11650/tjm/230101
Kaituo Liu, Jianzhong Lu, Jun Wu, Tian Yue
{"title":"Orlicz–Hardy Weak Martingale Spaces for Two-parameter","authors":"Kaituo Liu, Jianzhong Lu, Jun Wu, Tian Yue","doi":"10.11650/tjm/230101","DOIUrl":"https://doi.org/10.11650/tjm/230101","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42720400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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