摘要
Inthispaperwedeveloptwoconformingfiniteelementmethodsforafourthorderbi-waveequationarisingasasimplifiedGinzburg-Landau-typemodelford-wavesuperconductorsinabsenceofappliedmagneticfield.UnlikethebiharmonicoperatorA2,thebi-waveoperator□~2isnotanellipticoperator,sotheenergyspaceforthebi-waveequationismuchlargerthantheenergyspaceforthebiharmonicequation.Thisthenmakesitpossibletoconstructloworderconformingfiniteelementsforthebi-waveequation.However,theexistenceandconstructionofsuchfiniteelementsstronglydependsonthemesh.Inthepaper,wefirstcharacterizemeshconditionswhichallowandnotallowconstructionofloworderconformingfiniteelementsforapproximatingthebi-waveequation.Wethenconstructacubicandaquarticconformingfiniteelement.Itisprovedthatbothelementshavethedesiredapproximationproperties,andgiveoptimalordererrorestimatesintheenergynorm,suboptimal(andoptimalinsomecases)ordererrorestimatesintheH~1andL~2norm.Finally,numericalexperimentsarepresentedtoguagetheefficiencyoftheproposedfiniteelementmethodsandtovalidatethetheoreticalerrorbounds.
出版日期
2010年03月13日（中国期刊网平台首次上网日期，不代表论文的发表时间）
