A variational principle for adaptive approximation of ordinary differential equations

A variational principle for adaptive approximation of ordinary differential equations

Moon, Kyoung-Sook; Szepessy, Anders; Tempone, Raúl; Zouraris, Georgios E "A variational principle for adaptive approximation of ordinary differential equations." Numer. Math. 96 (2003), no. 1, 131–152.
Moon, Kyoung-Sook; Szepessy, Anders; Tempone, Raúl; Zouraris, Georgios E
A variational principle for adaptive approximation of ordinary differential equations
2003
A variational principle, inspired by optimal control, yields a simple derivation of an error representation, global error=∑local error⋅weight, for general approximation of functions of solutions to ordinary differential equations. This error representation is then approximated by a sum of computable error indicators, to obtain a useful global error indicator for adaptive mesh refinements. A uniqueness formulation is provided for desirable error representations of adaptive algorithms.
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