The paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media.We prove that the optimal L 2 err...The paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media.We prove that the optimal L 2 error estimates hold without any time-step(convergence)conditions,while all previous works require certain time-step restrictions.Theoretical analysis is based on a splitting of the error into two parts:the error from the time discretization of the PDEs and the error from the finite element discretization of the corresponding time-discrete PDEs,which was proposed in our previous work[26,27].Numerical results for both two and three-dimensional flow models are presented to confirm our theoretical analysis.展开更多
The present study describes the facile preparation of acid/CO2 stimuliresponsive sheddable nanoparticles based on carboxymethylated chitosan(CMCS).Commercially available CMCS was grafted with monomethoxy polyethylene ...The present study describes the facile preparation of acid/CO2 stimuliresponsive sheddable nanoparticles based on carboxymethylated chitosan(CMCS).Commercially available CMCS was grafted with monomethoxy polyethylene glycol(mPEG)chains via an acid/CO2 responsive linker,i.e.,benzoic-imine,and then was used for the cross-linking with CaCI2.With a high CMCS concentration up to 7 mg/mL,stable nanoparticles were successfully prepared.The particle size grew slightly with increasing the molecular weight of mPEG.When the concentration of CaCI2 and the feed ratio of CMCS to mPEG increased,the particle size decreased at first and then increased after reaching a minimum size.When the particles were stimulated by CO2 or acid,benzoic.imine cleaved quickly,and mPEG fell off the nanoparticles simultaneously,and then flocculation and precipitation occurred.These sheddable nanoparticles might have potential application in the biomedical field in eluding the intelligent drug delivery system.展开更多
This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is li...This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is limited mainly due to the lack of a fundamental Gronwall type inequality.In this paper,we establish such a fundamental inequality for the L1 approximation to the Caputo fractional derivative.In terms of the Gronwall type inequality,we provide optimal error estimates of several fully discrete linearized Galerkin finite element methods for nonlinear problems.The theoretical results are illustrated by applying our proposed methods to the time fractional nonlinear Huxley equation and time fractional Fisher equation.展开更多
基金supported in part by a grant from National Science Foundation(Project No.11301262)a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.CityU 102613)The work of J.Wang and W.Sun was supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.CityU 102613).
文摘The paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media.We prove that the optimal L 2 error estimates hold without any time-step(convergence)conditions,while all previous works require certain time-step restrictions.Theoretical analysis is based on a splitting of the error into two parts:the error from the time discretization of the PDEs and the error from the finite element discretization of the corresponding time-discrete PDEs,which was proposed in our previous work[26,27].Numerical results for both two and three-dimensional flow models are presented to confirm our theoretical analysis.
基金This work was supported by the Natural Science Foundation of Hubei Province(2016CFB329)the Science and Technology Research Program of Hubei Provincial Department of Education(B2016260)the Scientific Research and Technological Development Program of Jingmen City(YFYB2016021).
文摘The present study describes the facile preparation of acid/CO2 stimuliresponsive sheddable nanoparticles based on carboxymethylated chitosan(CMCS).Commercially available CMCS was grafted with monomethoxy polyethylene glycol(mPEG)chains via an acid/CO2 responsive linker,i.e.,benzoic-imine,and then was used for the cross-linking with CaCI2.With a high CMCS concentration up to 7 mg/mL,stable nanoparticles were successfully prepared.The particle size grew slightly with increasing the molecular weight of mPEG.When the concentration of CaCI2 and the feed ratio of CMCS to mPEG increased,the particle size decreased at first and then increased after reaching a minimum size.When the particles were stimulated by CO2 or acid,benzoic.imine cleaved quickly,and mPEG fell off the nanoparticles simultaneously,and then flocculation and precipitation occurred.These sheddable nanoparticles might have potential application in the biomedical field in eluding the intelligent drug delivery system.
基金This work is supported by NSFC(Grant Nos.11771035,11771162,11571128,61473126,91430216,91530204,11372354 and U1530401),a grant from the RGC of HK 11300517,China(Project No.CityU 11302915),China Postdoctoral Science Foundation under grant No.2016M602273,a grant DRA2015518 from 333 High-level Personal Training Project of Jiangsu Province,and the USA National Science Foundation grant DMS-1315259the USA Air Force Office of Scientific Research grant FA9550-15-1-0001.Jiwei Zhang also thanks the hospitality of Hong Kong City University during the period of his visiting.
文摘This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is limited mainly due to the lack of a fundamental Gronwall type inequality.In this paper,we establish such a fundamental inequality for the L1 approximation to the Caputo fractional derivative.In terms of the Gronwall type inequality,we provide optimal error estimates of several fully discrete linearized Galerkin finite element methods for nonlinear problems.The theoretical results are illustrated by applying our proposed methods to the time fractional nonlinear Huxley equation and time fractional Fisher equation.
