@TechReport{	  it:2011-017,
  author	= {Anna Nissen and Gunilla Kreiss and Margot Gerritsen},
  title		= {Stability at Nonconforming Grid Interfaces for a High
		  Order Discretization of the {S}chr{\"o}dinger Equation},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2011},
  number	= {2011-017},
  month		= aug,
  note		= {Typos corrected October 7, 2011.},
  abstract	= {In this paper we extend the results from our earlier work
		  on stable boundary closures for the Schr{\"o}dinger
		  equation using the summation-by-parts-simultaneous
		  approximation term (SBP--SAT) method to include stability
		  and accuracy at non-conforming grid interfaces. Stability
		  at the grid interface is shown by the energy method, and
		  the estimates are generalized to multiple dimensions. The
		  accuracy of the grid interface coupling is investigated
		  using normal mode analysis for operators of 2nd and 4th
		  order formal interior accuracy. We show that full accuracy
		  is retained for the 2nd and 4th order operators. The
		  accuracy results are extended to 6th and 8th order
		  operators by numerical simulations, in which case two
		  orders of accuracy is gained with respect to the lower
		  order approximation close to the interface.}
}