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Multi-adaptive Galerkin methods for ODEs I
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DOI：10.1137/S1064827501389722.png)
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摘要
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We present multi-adaptive versions of the standard continuous and discontinuous Galerkin methods for ODEs. Taking adaptivity one step further, we allow for individual timesteps, 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.
Keyword:
multi-adaptivity
individual time-steps
local time-steps
ODE
continuous Galerkin
discontinuous Galerkin
global error control
adaptivity
mcG(q)
mdG(q)
期刊
IF:
2.6
论文数:
5.1K
被引数:
1.8W
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