Pub Date : 2023-06-29DOI: 10.1007/s11425-022-2078-4
Jinye Shen, Fanhai Zeng, M. Stynes
{"title":"Second-order error analysis of the averaged L1 scheme $$overline {{rm{L1}}} $$ for time-fractional initial-value and subdiffusion problems","authors":"Jinye Shen, Fanhai Zeng, M. Stynes","doi":"10.1007/s11425-022-2078-4","DOIUrl":"https://doi.org/10.1007/s11425-022-2078-4","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"84 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89026360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-29DOI: 10.1007/s11425-022-2057-8
Junzhuo Gao, Lei Wang, Heng Lian
{"title":"Optimal decorrelated score subsampling for generalized linear models with massive data","authors":"Junzhuo Gao, Lei Wang, Heng Lian","doi":"10.1007/s11425-022-2057-8","DOIUrl":"https://doi.org/10.1007/s11425-022-2057-8","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"49 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88375757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-20DOI: 10.1007/s11425-022-2077-7
Gang Chen, Xiaoping Xie
In this paper, we analyze a class of globally divergence-free (and therefore pressure-robust) hybridizable discontinuous Galerkin (HDG) finite element methods for stationary Navier-Stokes equations. The methods use the $$cal{P}_{k}/cal{P}_{k-1}(kgeqslant 1)$$ discontinuous finite element combination for the velocity and pressure approximations in the interior of elements, piecewise $$cal{P}_{m}(m=k,k-1)$$ for the velocity gradient approximation in the interior of elements, and piecewise $$cal{P}_{k}/cal{P}_{k}$$ for the trace approximations of the velocity and pressure on the inter-element boundaries. We show that the uniqueness condition for the discrete solution is guaranteed by that for the continuous solution together with a sufficiently small mesh size. Based on the derived discrete HDG Sobolev embedding properties, optimal error estimates are obtained. Numerical experiments are performed to verify the theoretical analysis.
{"title":"Analysis of a class of globally divergence-free HDG methods for stationary Navier-Stokes equations","authors":"Gang Chen, Xiaoping Xie","doi":"10.1007/s11425-022-2077-7","DOIUrl":"https://doi.org/10.1007/s11425-022-2077-7","url":null,"abstract":"In this paper, we analyze a class of globally divergence-free (and therefore pressure-robust) hybridizable discontinuous Galerkin (HDG) finite element methods for stationary Navier-Stokes equations. The methods use the $$cal{P}_{k}/cal{P}_{k-1}(kgeqslant 1)$$ discontinuous finite element combination for the velocity and pressure approximations in the interior of elements, piecewise $$cal{P}_{m}(m=k,k-1)$$ for the velocity gradient approximation in the interior of elements, and piecewise $$cal{P}_{k}/cal{P}_{k}$$ for the trace approximations of the velocity and pressure on the inter-element boundaries. We show that the uniqueness condition for the discrete solution is guaranteed by that for the continuous solution together with a sufficiently small mesh size. Based on the derived discrete HDG Sobolev embedding properties, optimal error estimates are obtained. Numerical experiments are performed to verify the theoretical analysis.","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135238563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-19DOI: 10.1007/s11425-022-2085-3
R. Chen, Zhilei Liang, Dehua Wang, R. Xu
{"title":"On the inviscid limit of the compressible Navier-Stokes equations near Onsager’s regularity in bounded domains","authors":"R. Chen, Zhilei Liang, Dehua Wang, R. Xu","doi":"10.1007/s11425-022-2085-3","DOIUrl":"https://doi.org/10.1007/s11425-022-2085-3","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"497 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79148636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-19DOI: 10.1007/s11425-021-2063-0
Xiaoqing Chi, Hui Zhang, Xiaoyun Jiang
In this paper, we first establish a new fractional magnetohydrodynamic (MHD) coupled flow and heat transfer model for a generalized second-grade fluid. This coupled model consists of a fractional momentum equation and a heat conduction equation with a generalized form of Fourier law. The second-order fractional backward difference formula is applied to the temporal discretization and the Legendre spectral method is used for the spatial discretization. The fully discrete scheme is proved to be stable and convergent with an accuracy of O(τ2 + N−r), where τ is the time step-size and N is the polynomial degree. To reduce the memory requirements and computational cost, a fast method is developed, which is based on a globally uniform approximation of the trapezoidal rule for integrals on the real line. The strict convergence of the numerical scheme with this fast method is proved. We present the results of several numerical experiments to verify the effectiveness of the proposed method. Finally, we simulate the unsteady fractional MHD flow and heat transfer of the generalized second-grade fluid through a porous medium. The effects of the relevant parameters on the velocity and temperature are presented and analyzed in detail.
{"title":"The fast method and convergence analysis of the fractional magnetohydrodynamic coupled flow and heat transfer model for the generalized second-grade fluid","authors":"Xiaoqing Chi, Hui Zhang, Xiaoyun Jiang","doi":"10.1007/s11425-021-2063-0","DOIUrl":"https://doi.org/10.1007/s11425-021-2063-0","url":null,"abstract":"In this paper, we first establish a new fractional magnetohydrodynamic (MHD) coupled flow and heat transfer model for a generalized second-grade fluid. This coupled model consists of a fractional momentum equation and a heat conduction equation with a generalized form of Fourier law. The second-order fractional backward difference formula is applied to the temporal discretization and the Legendre spectral method is used for the spatial discretization. The fully discrete scheme is proved to be stable and convergent with an accuracy of O(τ2 + N−r), where τ is the time step-size and N is the polynomial degree. To reduce the memory requirements and computational cost, a fast method is developed, which is based on a globally uniform approximation of the trapezoidal rule for integrals on the real line. The strict convergence of the numerical scheme with this fast method is proved. We present the results of several numerical experiments to verify the effectiveness of the proposed method. Finally, we simulate the unsteady fractional MHD flow and heat transfer of the generalized second-grade fluid through a porous medium. The effects of the relevant parameters on the velocity and temperature are presented and analyzed in detail.","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135380346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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