Two kinds of Schwarz type domain decomposition methods are introduced to solve thegeneral selfadjoint second order parabolic partial differential equstions, and the dependence ofconvergence rate of these algorithms on...Two kinds of Schwarz type domain decomposition methods are introduced to solve thegeneral selfadjoint second order parabolic partial differential equstions, and the dependence ofconvergence rate of these algorithms on parameters of time-step and space-mesh is also analyzed.The convergence, independent of the iteration times at each time-level, of the approximate solution is proved and a priori optimal L2 error estimates are given.展开更多
In this paper, an existence result of entropy solutions to some parabolic problems is established. The data belongs to L^1 and no growth assumption is made on the lower-order term in divergence form.
Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Informatio...Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Information on the least-squares mixed element schemes for nonlinear parabolic problem.展开更多
In this paper, we consider the nonlocal problem of the formand the associated nonlocal stationary problemwhere λ is a positive parameter. For Ω to be an annulus, we prove that the nonlocal stationary problem has a u...In this paper, we consider the nonlocal problem of the formand the associated nonlocal stationary problemwhere λ is a positive parameter. For Ω to be an annulus, we prove that the nonlocal stationary problem has a unique solution if and only if λ 〈 2｜Ω｜2, and for λ = 2｜Ω｜2, the solution of the nonlocal parabolic problem grows up globally to infinity as t→∞.展开更多
We give an existence result of the obstacle parabolic equations3b（x,u） div（a（x,t,u, Vu））＋div（（x,t,u））=f in QT, 3twhere b（x,u） is bounded function ot u, the term atva,x,r,u, v u）） is a Letay type operat...We give an existence result of the obstacle parabolic equations3b（x,u） div（a（x,t,u, Vu））＋div（（x,t,u））=f in QT, 3twhere b（x,u） is bounded function ot u, the term atva,x,r,u, v u）） is a Letay type operator and the function is a nonlinear lower order and satisfy only the growth condition. The second term belongs to L1 （QT）. The proof of an existence solution is based on the penalization methods.展开更多
This paper deals with a parabolic system in a multi dimentional bounded domain ΩR n with the smooth boundary Ω. We discuss an inverse parabolic problem of determining the indirectly measurable internal heat distri...This paper deals with a parabolic system in a multi dimentional bounded domain ΩR n with the smooth boundary Ω. We discuss an inverse parabolic problem of determining the indirectly measurable internal heat distribution at any intermediate moment from the heat distribution measurements in arbitrary accessible subdomain ωΩ at some time interval. Our main result is the Hlder stability estimate in the inverse problem and the proof is completed with a Carleman estimate and a eigenfunction expansion for parabolic equations.展开更多
Partition property plays a central role in domain decomposition methods. Existing theory essentially assumes certain ellipticity. We prove the partition property for prod lems without ellipticity which are of practica...Partition property plays a central role in domain decomposition methods. Existing theory essentially assumes certain ellipticity. We prove the partition property for prod lems without ellipticity which are of practical importance. Example applications include implicit schemes applied to degenerate parabolic partial differential equations arising from superconductors, superfluids and liquid crystals. With this partition property, Schwarz algorithms can be applied to general non-elliptic problems with an h-independent optimal convergence rate. Application to the time-dependent Ginzburg-Landau model of superconductivity is illustrated and numerical results are presented.展开更多
A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approxi...A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.展开更多
文摘Two kinds of Schwarz type domain decomposition methods are introduced to solve thegeneral selfadjoint second order parabolic partial differential equstions, and the dependence ofconvergence rate of these algorithms on parameters of time-step and space-mesh is also analyzed.The convergence, independent of the iteration times at each time-level, of the approximate solution is proved and a priori optimal L2 error estimates are given.
文摘In this paper, an existence result of entropy solutions to some parabolic problems is established. The data belongs to L^1 and no growth assumption is made on the lower-order term in divergence form.
基金Major State Basic Research Program of People's Republic of China(G1999032803).
文摘Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Information on the least-squares mixed element schemes for nonlinear parabolic problem.
基金Supported by the Foundation for Young Talents in College of Anhui Province （Grant No. 2011SQRL115）, Program sponsored for Scientific Innovation Research of College Graduate in Jangsu Province （Grant No. 181200000649）, the courses building projects of Anhui Science and Technology University （Grant No. ZDKC1121）, the pre-research project of Anhui Science and Technology University （Grant No. ZRC2012308） and Training Fund of Xi＇an University of Science and TechnologyAcknowledgements The authors are grateful to the anonymous referees for their careful reading of the manuscript and numerous suggestions for its improvement.
文摘In this paper, we consider the nonlocal problem of the formand the associated nonlocal stationary problemwhere λ is a positive parameter. For Ω to be an annulus, we prove that the nonlocal stationary problem has a unique solution if and only if λ 〈 2｜Ω｜2, and for λ = 2｜Ω｜2, the solution of the nonlocal parabolic problem grows up globally to infinity as t→∞.
文摘We give an existence result of the obstacle parabolic equations3b（x,u） div（a（x,t,u, Vu））＋div（（x,t,u））=f in QT, 3twhere b（x,u） is bounded function ot u, the term atva,x,r,u, v u）） is a Letay type operator and the function is a nonlinear lower order and satisfy only the growth condition. The second term belongs to L1 （QT）. The proof of an existence solution is based on the penalization methods.
文摘This paper deals with a parabolic system in a multi dimentional bounded domain ΩR n with the smooth boundary Ω. We discuss an inverse parabolic problem of determining the indirectly measurable internal heat distribution at any intermediate moment from the heat distribution measurements in arbitrary accessible subdomain ωΩ at some time interval. Our main result is the Hlder stability estimate in the inverse problem and the proof is completed with a Carleman estimate and a eigenfunction expansion for parabolic equations.
基金This work was supported in part by Hong Kong RGC DAG93/94 SC10, Competitive Earmarked ResearchGrant HKUST593/94E and the speci
文摘Partition property plays a central role in domain decomposition methods. Existing theory essentially assumes certain ellipticity. We prove the partition property for prod lems without ellipticity which are of practical importance. Example applications include implicit schemes applied to degenerate parabolic partial differential equations arising from superconductors, superfluids and liquid crystals. With this partition property, Schwarz algorithms can be applied to general non-elliptic problems with an h-independent optimal convergence rate. Application to the time-dependent Ginzburg-Landau model of superconductivity is illustrated and numerical results are presented.
文摘A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.
