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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
computer science
On the order of accuracy for difference approximations of initial-boundary value problems
Journal of Computational Physics, Volume 218, No. 1, Year 2006
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Description
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. © 2006 Elsevier Inc. All rights reserved.
Authors & Co-Authors
Svärd, Magnus
United States, Palo Alto
Stanford University
Sweden, Uppsala
Uppsala Universitet
Nordström, Jan
Sweden, Uppsala
Uppsala Universitet
Sweden, Kista
Totalforsvarets Forskningsinstitut
Statistics
Citations: 215
Authors: 2
Affiliations: 3
Identifiers
Doi:
10.1016/j.jcp.2006.02.014
ISSN:
00219991