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A SINGLE STEP SCHEME WITH HIGH ACCURACY FOR parabolic problem

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Acta Mathematica Scientia 2001年第2期21卷 237-242页

作者：陈传淼胡志刚 Institute of Computation Hunan Normal University Changsha 410081 China

A single step scheme with high accuracy for solving parabolic problem is proposed. It is shown that this scheme possesses good stability and fourth order accuracy with respect to both time and space variables, which a... 详细信息

关键词： parabolic problem single step scheme fourth order accuracy

TIME-EXTRAPOLATION ALGORITHM （TEA） FOR LINEAR parabolic problemS

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Journal of Computational Mathematics 2014年第2期32卷 183-194页

作者： Hongling Hu Chuanmiao Chen Kejia Pan College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China) Hunan Normal University Changsha 410081 China School of Mathematics and Statistics Central South University Changsha 410083 China

The fast solutions of Crank-Nicolson scheme on quasi-uniform mesh for parabolic prob- lems are discussed. First, to decrease regularity requirements of solutions, some new error estimates are proved. Second, we analyze the two characteristics of parabolic discrete scheme, and find that the efficiency of Multigrid Method （MG） is greatly reduced. Nu- merical experiments compare the efficiency of Direct Conjugate Gradient Method （DCG） and Extrapolation Cascadic Multigrid Method （EXCMG）. Last, we propose a Time- Extrapolation Algorithm （TEA）, which takes a linear combination of previous several level solutions as good initial values to accelerate the rate of convergence. Some typical extrapolation formulas are compared numerically. And we find that under certain accuracy requirement, the CG iteration count for the 3-order and 7-level extrapolation formula is about 1/3 of that of DCG＇s. Since the TEA algorithm is independent of the space dimension, it is still valid for quasi-uniform meshes. As only the finest grid is needed, the proposed method is regarded very effective for nonlinear parabolic problems.

关键词： parabolic problem Crank-Nicolson scheme Error estimates Time-extrapolationalgorithm CG-iteration.

ON L2 ERROR ESTIMATE FOR WEAK GALERKIN FINITE ELEMENT METHODS FOR parabolic problemS

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Journal of Computational Mathematics 2014年第2期32卷 195-204页

作者： Fuzheng Gao Lin Mu School of Mathematics Shandong University Jinan Shandong 250100 China Department of Mathematics Michigan State University East Lansing MI 48824 USA

A weak Galerkin finite element method with stabilization term, which is symmetric, positive definite and parameter free, was proposed to solve parabolic equations by using weakly defined gradient operators over discontinuous functions. In this paper, we derive the optimal order error estimate in L2 norm based on dual argument. Numerical experiment is conducted to confirm the theoretical results.

关键词： WG-FEMs discrete weak gradient parabolic problem error estimate.

A POSTERIORI ERROR ESTIMATES OF FINITEELEMENT METHOD FOR parabolic problemS

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Acta Mathematica Scientia 1999年第4期19卷 449-456页

作者：陈艳萍 Department of Mathematics Xiangtan University Xiangtan 411105 China Department of Mathematics Nanjing University Nanjing 210008 China

This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the p... 详细信息

关键词： Aposteriori error estimates finite element method parabolic problem

Cascadic multigrid methods for parabolic problems

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Science China Mathematics 2008年第8期51卷 1415-1439页

作者： DU Qiang MING PingBing Department of Mathematics Pennsylvania State UniversityUniversity ParkPA 16802USA LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAMSSChinese Academy of SciencesBeijing 100190China

In this paper,we consider the cascadic multigrid method for a parabolic type *** Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the *** new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular *** error bound sare derived for both smooth and non-smooth *** strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.

关键词： cascadic multigrid method parabolic problem finite element methods backward Euler scheme smoother stability optimal error order optimal complexity 65N30 65N55 65F10

Natural Boundary Element Method for parabolicEquations in an Unbounded Domain

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Journal of Mathematical Research and Exposition 2002年第2期22卷 177-188页

作者：朱昌杰杜其奎淮北煤炭师范学院安徽淮北235000 南京师范大学数学与计算机科学学院江苏南京210097

In this paper we introduce an implementation for the efficient numericalsolution of exterior initial boundary value problem for parabolic equation. The problemis reformulated as an equivalent one on a boundary T using natural boundary *** governing equation is first discretized in time, leading to a time-stepping scheme,where an exterior elliptic problem has to be solved in each time step. By Fourier ex-pansion, we derive a natural integral equation of the elliptic problem related to timestep and Poisson integral integral formula over exterior circular domain. Finite elementdiscretization of the natural integral equation is employed to solve this problem. Thecomputational aspects of this method are discussed. Numerical results are presented toillustrate feasibility and efficiency of our method.

关键词： parabolic problem natural boundary reduction exterior problem numer-ical implementation finite element.

Avoidance of Blow-up by Moving Medium

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Chinese Quarterly Journal of Mathematics 2005年第2期20卷 167-177页

作者： YAOLi LIUYun-xian YANGPeng-fei DepartmentofAppliedMathematics InformationEngineeringUniversityZhengzhou450002China CollegeofMathematics ShandongUniversityJinan250100China

This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place only at a single point. We show that under some conditions, the solution blows up in finite time and the blow-up set is the whole spherical medium. When the spherical medium is allowed to move in a special space, we investigate another parabolic initial-boundary value problem. It is proved that the blow-up can be avoided if the acceleration of the motion satisfies certain conditions.

关键词： moving medium blow-up parabolic problem