摘要
Inthisarticlewedefineasurfacefiniteelementmethod(SFEM)forthenumericalsolutionofparabolicpartialdifferentialequationsonhypersurfacesFinR~(n+1).ThekeyideaisbasedontheapproximationofFΓbyapolyhedralsurfaceΓ_hconsistingofaunionofsimplices(trianglesforn=2,intervalsforn=1)withverticesonF.AfiniteelementspaceoffunctionsisthendefinedbytakingthecontinuousfunctionsonΓ_hwhicharelinearaffineoneachsimplexofthepolygonalsurface.WeusesurfacegradientstodefineweakformsofellipticoperatorsandnaturallygenerateweakformulationsofellipticandparabolicequationsonΓ.Ourfiniteelementmethodisappliedtoweakformsoftheequations.Thecomputationofthemassandelementstiffnessmatricesaresimpleandstraightforward.Wegiveanexampleoferrorboundsinthecaseofsemi-discretizationinspaceforafourthorderlinearproblem.Numericalexperimentsaredescribedforseverallinearandnonlinearpartialdifferentialequations.Inparticularthepowerofthemethodisdemonstratedbyemployingit,tosolvehighlynonlinearsecondandfourthorderproblemssuchassurfaceAllen-CahnandCahn-Hilliardequationsandsurfacelevelsetequationsforgeodesicmeancuryatureflow.
出版日期
2007年04月14日（中国期刊网平台首次上网日期，不代表论文的发表时间）
