学科分类
/ 1
2 个结果
  • 简介:Inthisarticlewedefineasurfacefiniteelementmethod(SFEM)forthenumericalsolutionofparabolicpartialdifferentialequationsonhypersurfacesFinR~(n+1).ThekeyideaisbasedontheapproximationofFΓbyapolyhedralsurfaceΓ_hconsistingofaunionofsimplices(trianglesforn=2,intervalsforn=1)withverticesonF.AfiniteelementspaceoffunctionsisthendefinedbytakingthecontinuousfunctionsonΓ_hwhicharelinearaffineoneachsimplexofthepolygonalsurface.WeusesurfacegradientstodefineweakformsofellipticoperatorsandnaturallygenerateweakformulationsofellipticandparabolicequationsonΓ.Ourfiniteelementmethodisappliedtoweakformsoftheequations.Thecomputationofthemassandelementstiffnessmatricesaresimpleandstraightforward.Wegiveanexampleoferrorboundsinthecaseofsemi-discretizationinspaceforafourthorderlinearproblem.Numericalexperimentsaredescribedforseverallinearandnonlinearpartialdifferentialequations.Inparticularthepowerofthemethodisdemonstratedbyemployingit,tosolvehighlynonlinearsecondandfourthorderproblemssuchassurfaceAllen-CahnandCahn-Hilliardequationsandsurfacelevelsetequationsforgeodesicmeancuryatureflow.

  • 标签: 表面偏微分方程 表面有限元法 测地曲率 三角形表面 抛物线方程