A variational principle for adaptive approximation of ordinary differential equations |
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Authors: | Email author" target="_blank">Kyoung-Sook?MoonEmail author Anders?Szepessy Raúl?Tempone Georgios E?Zouraris |
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Institution: | (1) Institutionen för Numerisk Analys och Datalogi, Kungl Tekniska Högskolan, 100 44 Stockholm, Sweden;(2) Matematiska Institutionen, Kungl Tekniska Högskolan, 100 44 Stockholm, Sweden;(3) Department of Mathematics, IACM, FO.R.T.H, University of the Aegean, 832 00, 711 10 Karlovassi, Heraklion, Samos, Greece |
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Abstract: | Summary 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.
Mathematics Subject Classification (2000): 65L70, 65G50This work has been supported by the EU–TMR project HCL # ERBFMRXCT960033, the EU–TMR grant # ERBFMRX-CT98-0234 (Viscosity Solutions and their Applications), the Swedish Science Foundation, UdelaR and UdeM in Uruguay, the Swedish Network for Applied Mathematics, the Parallel and Scientific Computing Institute (PSCI) and the Swedish National Board for Industrial and Technical Development (NUTEK). |
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