@TechReport{ it:2003-061,
author = {Lars Ferm and Per L{\"o}tstedt},
title = {Space-Time Adaptive Solution of First Order {PDE}s},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2003},
number = {2003-061},
month = dec,
abstract = {An explicit time-stepping method is developed for adaptive
solution of time-dependent partial differential equations
with first order derivatives. The space is partitioned into
blocks and the grid is refined and coarsened in these
blocks. The equations are integrated in time by a
Runge-Kutta-Fehlberg method. The local errors in space and
time are estimated and the time and space steps are
determined by these estimates. The error equation is
integrated to obtain global errors of the solution. The
method is shown to be stable if one-sided space
discretizations are used. Examples such as the wave
equation, Burgers' equation, and the Euler equations in one
space dimension with discontinuous solutions illustrate the
method.}
}