@TechReport{	  it:2000-023,
  author	= {Per L{\"o}tstedt and Stefan S{\"o}derberg and Alison
		  Ramage and Lina Hemmingsson-Fr{\"a}nd{\'e}n},
  title		= {Implicit solution of hyperbolic equations with space-time
		  adaptivity},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2000},
  number	= {2000-023},
  month		= sep,
  abstract	= {Adaptivity in space and time is introduced to control the
		  error in the numerical solution of hyperbolic partial
		  differential equations. The equations are discretised by a
		  finite volume method in space and an implicit linear
		  multistep method in time. The computational grid is refined
		  in blocks. At the boundaries of the blocks, there may be
		  jumps in the step size. Special treatment is needed there
		  to ensure second order accuracy and stability. The local
		  truncation error of the discretisation is estimated and is
		  controlled by changing the step size and the time step. The
		  global error is obtained by integration of the error
		  equations. In the implicit scheme, the system of linear
		  equations at each time step is solved iteratively by the
		  GMRES method. Numerical examples executed on a parallel
		  computer illustrate the method. }
}