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

  • Authors:

  • Magnus Svärd;Jan Nordström

  • Affiliations:

  • Center for Turbulence Research, Stanford University, Stanford, CA and Department of Information Technology, Uppsala University, Uppsala, Sweden;Department of Information Technology, Uppsala University, Uppsala, Sweden and Computational Physics Department, Division of Systems Technology, The Swedish Defence Research Agency, Stockholm, Swed ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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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.