Multi-adaptive Galerkin methods for ODEs I
Artikel i vetenskaplig tidskrift, 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

Författare

Anders Logg

Chalmers, Institutionen för beräkningsmatematik

Göteborgs universitet

SIAM Journal of Scientific Computing

1064-8275 (ISSN) 1095-7197 (eISSN)

Vol. 24 1879-1902

Ämneskategorier

Beräkningsmatematik

DOI

10.1137/S1064827501389722