@TechReport{	  it:2010-030,
  author	= {Jens Lindstr{\"o}m and Jan Nordstr{\"o}m},
  title		= {Spectral Analysis of the Continuous and Discretized Heat
		  and Advection Equation on Single and Multiple Domains},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2010},
  number	= {2010-030},
  month		= dec,
  abstract	= {In this paper we study the heat and advection equation in
		  single and multiple domains. We discretize using a second
		  order accurate finite difference method on
		  Summation-By-Parts form with weak boundary and interface
		  conditions. We derive analytic expressions for the spectrum
		  of the continuous problem and for their corresponding
		  discretization matrices. We show how the spectrum of the
		  single domain operator is contained in the multi domain
		  operator spectrum when artificial interfaces are
		  introduced. We study the impact on the spectrum and
		  discretization errors depending on the interface treatment
		  and verify that the results are carried over to higher
		  order accurate schemes.}
}