Acta mathematica scientia,Series A ›› 2001, Vol. 21 ›› Issue (2): 201-210.
• Articles • Previous Articles Next Articles
CHEN Wei
Online:
Published:
Supported by:
国家自然科学基金资助项目,国家教委博士点基金资助项目
Abstract:
考虑数值求解具有对流项的高维拟线性Sobolev方程,构造了特征有限元格式,提出用交替方向预处理迭代法求特征有限元格式在每一时间步所产生的代数方程组的近似解,整个计算过程仅对一个可方向交替的预处理矩阵求逆一次,大大降低了计算量.证明了迭代解的最佳L^2模误差估计,并给出了算法的拟优工作量估计.
Key words: 特征有限元, 交替方向, 预处理迭代
CLC Number:
CHEN Wei. A.D.P.I. Approximation for Characteristic Finite Element Methods for Quasilinear Sobolev Equations and Its Analysis[J].Acta mathematica scientia,Series A, 2001, 21(2): 201-210.
0 / / Recommend
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
URL: http://121.43.60.238/sxwlxbA/EN/
http://121.43.60.238/sxwlxbA/EN/Y2001/V21/I2/201
1 BarenblattGI,BonaJL,KochinaIN.Basicconceptsinthetheoryofseepageofhomogeneousliquidsinfissuresrocks.JApplMath Mech,1960,24:1286-1303 2 TingT W.Acoolingprocessaccordingtotwotemperaturetheoryofheatconduction.JMathAnalAppl,1974,45:23-31 3 TingT W.Certainnonsteadyflowsofsecondorderfluids.ArchRationalMechAnal,1963,14:1-26 4 施德明.非线性湿气迁移方程的初边值问题.应用数学学报,1990,13:12-38 5 TalorD W.Researchonconsolidationofclay.Cambridge:MITpress,1952 6 DavisPL.Aquasilinearparabolicandarelatedthirdorderproblem.JMathAnalAppl,1970,49:327-335 7 EwingRE.AcouplednonlinearhyperbolicSobolevsystem .Ann MatPuraApplSerIV,1977,114:331-349 8 EwingRE.TimesteppinggalerkinmethodfornonlinearSobolevpartialdifferentialequations.SIAMJNumerAnal,1978,15:1125-1150 9 LinYP,ZhangTie.FiniteelementmethodsfornonlinearSobolevequationswithnonlinearboundarycondition.JMathAnalandAppl,1992,165:180-191 10 由同顺.非线性Sobolev方程的特征-差分方法.计算数学,1995,17:13-27 11 DouglasJJR,RussellT F.Numericalmethodsforconvectiondominateddiffusionproblemsbasedoncombingthemethodofcharacteristicswithfiniteelementorfinitedifferenceprocedures.SIAMJNumerAnal,1982,19:871-885 12 RussellTF.Timesteppingalongcharacteristicswithincompleteiterationforagalerkinapproximationofmiscibledisplacementinporousmedia.SIAMJNumerAnal,1985,22:970-1013 13 DouglasJJrandDoupontT.AlternatingDirectiongalerkinmethodsonrectangles.In:B.Hubbarded.ProcsymposiumonnumericalsolutionofpartialdifferentialequationsII.New York:Academicpress,1971.133-224 14 DendyGE,FairweatherG.AlternatingDirectiongalerkinmethodsforparabolicandhyperbolicproblemsonrectan gularpolygons.SIAMJNumerAnal,1975,12:144-163 15 HayesLJ.GalerkinAlternatingDirectionmethodsfornonrectangularregionsusingpatchapproximations.SIAMJ NumerAnal,1981,18:627-643 16 BrambleJ,EwingR,LiGang.Alternatingdirectionmultistepmethodsforparabolicproblemsiterativestabilization.SIAMJNumerAnal,1989,26:904-919 17 GeorgeJA.Nesteddissectiononaregularfiniteelementmesh.SIAMJNumerAnal,1973,10:345-363
Cited
Existence of Positive Periodic Solutions of a Prey-Predator
System with Several Delays
A Spectral Characterization for Stability of C0-semigroups
on ∑e1 Type Banach Spaces