Space---Time Adaptive Solution of First Order PDES

Authors:
Lars Ferm;Per Lötstedt
Affiliations:
Department of Information Technology, Division of Scientific Computing, Uppsala University, Uppsala, Sweden SE-75105;Department of Information Technology, Division of Scientific Computing, Uppsala University, Uppsala, Sweden SE-75105
Venue:
Journal of Scientific Computing
Year:
2006

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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 (RKF) method. The local errors in space and time are estimated and the time and space steps are determined by these estimates. 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.