Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {M.~Griebel and D.~Oeltz},
  title = {A Sparse Grid Space-Time Discretization Scheme for
		  Parabolic Problems},
  journal = {Computing},
  year = {2007},
  volume = {81},
  number = {1},
  pages = {1--34},
  issn = {0010-485X},
  abstract = {In this paper we consider the discretization in space and
		  time of parabolic differential equations where we use the
		  so-called space-time sparse grid technique. It employs the
		  tensor product of a one-dimensional multilevel basis in
		  time and a proper multilevel basis in space. This way, the
		  additional order of complexity of a direct space-time
		  discretization can be avoided, provided that the solution
		  fulfills a certain smoothness assumption in space-time,
		  namely that its mixed space-time derivatives are bounded.
		  This holds in many applications due to the smoothing
		  properties of the propagator of the parabolic PDE (heat
		  kernel). In the more general case, the space-time sparse
		  grid approach can be employed together with adaptive
		  refinement in space and time and then leads to similar
		  approximation rates as the non-adaptive method for smooth
		  We analyze the properties of different space-time sparse
		  grid discretizations for parabolic differential equations
		  from both, the theoretical and practical point of view,
		  discuss their implementational aspects and report on the
		  results of numerical experiments.},
  ps = { 1},
  annote = {article,C2}