@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. }
}