Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization

<html xmlns:o=3D"urn:schemas-microsoft-com:office:office" xmlns:w=3D"urn:schemas-microsoft-com:office:word" xmlns=3D"http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dwindows-1252"> <meta name=3DProgId content=3DWord.Document> <meta name=3DGenerator content=3D"Microsoft Word 11"> <meta name=3DOriginator content=3D"Microsoft Word 11"> <link rel=3DFile-List href=3D"RESUMEN_archivos/filelist.xml"> RESUMEN <!--[if gte mso 9]><xml> <o:DocumentProperties> <o:Author>Biblioteca de Ciencias y Tecnología</o:Author> <o:Template>Normal</o:Template> <o:LastAuthor>Biblioteca de Ciencias y Tecnología</o:LastAuthor> <o:Revision>3</o:Revision> <o:TotalTime>15</o:TotalTime> <o:Created>2006-05-19T14:19:00Z</o:Created> <o:LastSaved>2006-05-19T14:54:00Z</o:LastSaved> <o:Pages>1</o:Pages> <o:Words>68</o:Words> <o:Characters>380</o:Characters> <o:Company>UCLA</o:Company> <o:Lines>3</o:Lines> <o:Paragraphs>1</o:Paragraphs> <o:CharactersWithSpaces>447</o:CharactersWithSpaces> <o:Version>11.6360</o:Version> </o:DocumentProperties> </xml><![endif]--><!--[if gte mso 9]><xml> <w:WordDocument> <w:SpellingState>Clean</w:SpellingState> <w:GrammarState>Clean</w:GrammarState> <w:HyphenationZone>21</w:HyphenationZone> <w:PunctuationKerning/> <w:DrawingGridHorizontalSpacing>6 pto</w:DrawingGridHorizontalSpacing> <w:DisplayHorizontalDrawingGridEvery>2</w:DisplayHorizontalDrawingGridEvery> <w:DisplayVerticalDrawingGridEvery>2</w:DisplayVerticalDrawingGridEvery> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState=3D"false" LatentStyleCount=3D"156"> </w:LatentStyles> </xml><![endif]--> <style> <!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} span.SpellE {mso-style-name:""; mso-spl-e:yes;} @page Section1 {size:612.1pt 792.1pt; margin:4.0cm 3.0cm 3.0cm 3.0cm; mso-header-margin:35.45pt; mso-footer-margin:35.45pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> </style> <!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabla normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman"; mso-ansi-language:#0400; mso-fareast-language:#0400; mso-bidi-language:#0400;} </style> <![endif]--> </head> <body lang=3DES style=3D'tab-interval:35.4pt'> RESUMEN<o:p></o:p> This paper provides an error analysis for the Crank–Nicolson method of time discretization applied to spatially discrete Galerkin approximations of the nonstationary Navier–Stokes equations. Second-order error estimates are proven locally in time under realistic assumptions about the regularity of the solution. For approximations of an exponentially stable solution, these local error estimates are extended uniformly in time as t → ∞. <o:p></o:p> <o:p> </o:p> </body> </html>