Journal of Scientific Computing

, Volume 26, Issue 1, pp 83–110 | Cite as

Space–Time Adaptive Solution of First Order PDES

  • Lars FermEmail author
  • Per Lötstedt


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.


Runge–Kutta–Fehlberg method shock problems space adaptation time adaptation 

AMS subject classification

65M20 65M50 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Information Technology, Division of Scientific ComputingUppsala UniversityUppsalaSweden

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