A multilevel finite element method in space-time for the Navier-Stokes problem

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Detail(s)

Original languageEnglish
Pages (from-to)1052-1078
Journal / PublicationNumerical Methods for Partial Differential Equations
Volume21
Issue number6
Publication statusPublished - Nov 2005

Abstract

A multilevel finite element method in space-time for the two-dimensional nonstationary Navier-Stokes problem is considered. The method is a multi-scale method in which the fully nonlinear Navier-Stokes problem is only solved on a single coarsest space-time mesh; subsequent approximations are generated on a succession of refined space-time meshes by solving a linearized Navier-Stokes problem about the solution on the previous level. The a priori estimates and error analysis are also presented for the J-level finite element method. We demonstrate theoretically that for an appropriate choice of space and time mesh widths: hj ∼ hj-13/2, kj ∼ kj-13/2, j = 2, . . . , J, the J-level finite element method in space-time provides the same accuracy as the one-level method in space-time in which the fully nonlinear Navier-Stokes problem is solved on a final finest space-time mesh. © 2005 Wiley Periodicals, Inc.

Research Area(s)

  • Error estimate, Multi-level finite element, Navier-Stokes problem, Space-time mesh