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

RESUMEN Biblioteca de Ciencias y Tecnología Normal Biblioteca de Ciencias y Tecnología 3 15 2006-05-19T14: 19: 00Z 2006-05-19T14: 54: 00Z 1 68 380 UCLA 3 1 447 11. 6360 Clean Clean 21 6 pto 2 2 false false false MicrosoftInternetExplorer4 /* 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; RESUMEN 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 → ∞.