@TechReport{	  it:2009-014,
  author	= {Mark H. Carpenter and Jan Nordstr{\"o}m and David
		  Gottlieb},
  title		= {Revisiting and Extending Interface Penalties for
		  Multi-Domain Summation-by-Parts Operators},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2009},
  number	= {2009-014},
  month		= may,
  abstract	= {A general interface procedure is presented for
		  multi-domain collocation methods satisfying the
		  summation-by-parts (SBP) spatial discretization convention.
		  Unlike more traditional operators (e.g. FEM) applied to the
		  advection-diffusion equation, the new procedure penalizes
		  the solution and the first p derivatives across the
		  interface. The combined interior/interface operators are
		  proven to be pointwise stable, and conservative, although
		  accuracy deteriorates for p>=2. Penalties between two
		  different sets of variables are compared (motivated by FEM
		  primal and flux formulations), and are shown to be
		  equivalent for certain choices of penalty parameters.
		  Extensive validation studies are presented using two
		  classes of high-order SBP operators: 1) central finite
		  difference, and 2) Legendre spectral collocation.}
}