Multi-adaptive Galerkin methods for ODEs I
Journal article, 2003
We present multi-adaptive versions of the standard continuous and discontinuous Galerkin methods for ODEs. Taking adaptivity one step further, we allow for individual time-steps, order and quadrature, so that in particular each individual component has its own time-step sequence. This paper contains a description of the methods, an analysis of their basic properties, and a posteriori error analysis. In the accompanying paper [A. Logg, SIAM J. Sci. Comput., submitted], we present adaptive algorithms for time-stepping and global error control based on the results of the current paper.
Individual time-steps
McG(q)
ODE
MdG(q)
Continuous Galerkin
Discontinuous Galerkin
Local time-steps
Multi-adaptivity
Adaptivity
Global error control
Author
Anders Logg
Chalmers, Department of Computational Mathematics
University of Gothenburg
SIAM Journal of Scientific Computing
1064-8275 (ISSN) 1095-7197 (eISSN)
Vol. 24 6 1879-1902Subject Categories
Computational Mathematics
DOI
10.1137/S1064827501389722