On the order of accuracy for difference approximations of initial-boundary value problems
2006 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 218, no 1, 333-352 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2006. Vol. 218, no 1, 333-352 p.
order of accuracy, stability, parabolic partial differential equations, Navier-Stokes equations, finite difference methods, summation-by-parts, boundary conditions, boundary closure, convergence rate
IdentifiersURN: urn:nbn:se:kth:diva-16089ISI: 000241565300016OAI: oai:DiVA.org:kth-16089DiVA: diva2:334131
QC 201005252010-08-052010-08-05Bibliographically approved