Fully Adaptive Multiscale Schemes for Conservation Laws Employing Locally Varying Time Stepping

Authors:
Siegfried Müller;Youssef Stiriba
Affiliations:
Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Aachen, Germany 52056;Departament Enginyeria Mecànica, Universitat "Rovira i Virgili" - ETSEQ, Tarragona, Spain 43007
Venue:
Journal of Scientific Computing
Year:
2007

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Abstract

In recent years the concept of fully adaptive multiscale finite volume schemes for conservation laws has been developed and analytically investigated. Here the grid adaptation is performed by means of a multiscale analysis. So far, all cells are evolved in time using the same time step size. In the present work this concept is extended incorporating locally varying time stepping. A general strategy is presented for explicit as well as implicit time discretization. The efficiency and the accuracy of the proposed concept is verified numerically.