Error analysis of the L2 least-Squares finite element method for incompressible inviscid rotational flows

Chiung Chiou Tsai, Suh Yuh Yang

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Abstract

In this article we analyze the L2 least-squares finite element approximations to the incompressible inviscid rotational flow problem, which is recast into the velocity-vorticity-pressure formulation. The least-squares functional is defined in terms of the sum of the squared L2 norms of the residual equations over a suitable product function space. We first derive a coercivity type a priori estimate for the first-order system problem that will play the crucial role in the error analysis. We then show that the method exhibits an optimal rate of convergence in the H1 norm for velocity and pressure and a suboptimal rate of convergence in the L2 norm for vorticity. A numerical example in two dimensions is presented, which confirms the theoretical error estimates.

Original languageEnglish
Pages (from-to)831-842
Number of pages12
JournalNumerical Methods for Partial Differential Equations
Volume20
Issue number6
DOIs
StatePublished - Nov 2004

Keywords

  • Euler equations
  • Incompressible inviscid rotational flows
  • Least-squares finite element methods
  • Standing vortex problems
  • Velocity-vorticity-pressure formulation

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