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On the order of accuracy for difference approximations of initial-boundary value problems

Svärd, Magnus ; Nordström, Jan

Journal of Computational Physics, 2006, Vol.218(1), pp.333-352 [Periódico revisado por pares]

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  • Título:
    On the order of accuracy for difference approximations of initial-boundary value problems
  • Autor: Svärd, Magnus ; Nordström, Jan
  • Assuntos: Order of Accuracy ; Stability ; Parabolic Partial Differential Equations ; Navier–Stokes Equations ; Finite Difference Methods ; Summation-By-Parts ; Boundary Conditions ; Boundary Closure ; Applied Sciences
  • É parte de: Journal of Computational Physics, 2006, Vol.218(1), pp.333-352
  • Descrição: To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jcp.2006.02.014 Byline: Magnus Svard (a)(b), Jan Nordstrom (b)(c) Keywords: Order of accuracy; Stability; Parabolic partial differential equations; Navier-Stokes equations; Finite difference methods; Summation-by-parts; Boundary conditions; Boundary closure Abstract: Finite difference approximations of the second derivative in space appearing in, parabolic, incompletely parabolic systems of, and 2nd-order hyperbolic, partial differential equations are considered. If the solution is pointwise bounded, we prove that finite difference approximations of those classes of equations can be closed with two orders less accuracy at the boundary without reducing the global order of accuracy. This result is generalised to initial-boundary value problems with an mth-order principal part. Then, the boundary accuracy can be lowered m orders. Further, it is shown that schemes using summation-by-parts operators that approximate second derivatives are pointwise bounded. Linear and nonlinear computations, including the two-dimensional Navier-Stokes equations, corroborate the theoretical results. Author Affiliation: (a) Center for Turbulence Research, Building 500, Stanford University, Stanford, CA 94305-3035, USA (b) Department of Information Technology, Uppsala University, SE-751 05 Uppsala, Sweden (c) Computational Physics Department, Division of Systems Technology, The Swedish Defence Research Agency, SE-164 90 Stockholm, Sweden Article History: Received 1 November 2005; Revised 14 February 2006; Accepted 15 February 2006
  • Idioma: Inglês

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