@TechReport{	  it:2018-002,
  author	= {Pietro Benedusi and Carlo Garoni and Rolf Krause and
		  Xiaozhou Li and Stefano Serra-Capizzano},
  title		= {Discontinuous {G}alerkin Discretization of the Heat
		  Equation in Any Dimension: the Spectral Symbol},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2018},
  number	= {2018-002},
  month		= jan,
  abstract	= {The multidimensional heat equation, along with its more
		  general version involving variable diffusion coefficients,
		  is discretized by a discontinuous Galerkin (DG) method in
		  time and a finite element (FE) method of arbitrary
		  regularity in space. We show that the resulting space-time
		  discretization matrices enjoy an asymptotic spectral
		  distribution as the mesh fineness increases, and we
		  determine the associated spectral symbol, i.e., the
		  function that carefully describes the spectral
		  distribution. The analysis of this paper is carried out in
		  a stepwise fashion, without omitting details, and it is
		  supported by several numerical experiments. It is
		  preparatory to the development of specialized solvers for
		  linear systems arising from the DG/FE approximation of the
		  heat equation in the case of both constant and variable
		  diffusion coefficients.}
}