@TechReport{ it:2004-040,
author = {Magnus Sv{\"a}rd and Jan Nordstr{\"o}m},
title = {On the Order of Accuracy for Difference Approximations of
Initial-Boundary Value Problems},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2004},
number = {2004-040},
month = sep,
abstract = {Finite difference approximations of the second derivative
in space appearing in, parabolic, incompletely parabolic
systems of, and second 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 $m$th order principal part. Then, the
boundary accuracy can be lowered $m$ orders.
Further, it is shown that summation-by-parts operators with
approximating second derivatives are pointwise bounded.
Linear and nonlinear computations corroborates the
theoretical results.}
}