AN UNFITTED hp-INTERFACE PENALTY FINITE ELEMENT METHOD FOR ELLIPTIC INTERFACE PROBLEMS

【摘要】Anhpversionofinterfacepenaltyfiniteelementmethod(hp-IPFEM)isproposedtosolvetheellipticinterfaceproblemsintwoandthreedimensionsonunfittedmeshes.ErrorestimatesinbrokenH1norm；whichareoptimalwithrespecttohandsuboptimalwithrespecttopbyhalfanorderofp；arederived.Bothsymmetricandnon-symmetricIPFEMareconsidered.ErrorestimatesinL^2normareprovedbythedualityargument.Alltheestimatesareindependentofthelocationoftheinterfacerelativetothemeshes.Numericalexamplesareprovidedtoillustratetheperformanceofthemethod.ThispaperisadaptedfromtheworkoriginallypostonarXiv.combythesameauthors(arXiv:1007.2893v1).