A variational principle for adaptive approximation of ordinary differential equations

Kyoung Sook Moon; Anders Szepessy; Raúl Tempone; Georgios E. Zouraris

doi:10.1007/s00211-003-0467-8

A variational principle for adaptive approximation of ordinary differential equations

Kyoung Sook Moon^*, Anders Szepessy, Raúl Tempone, Georgios E. Zouraris

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

A variational principle, inspired by optimal control, yields a simple derivation of an error representation, global error = Σ 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.

Original language	English (US)
Pages (from-to)	131-152
Number of pages	22
Journal	Numerische Mathematik
Volume	96
Issue number	1
DOIs	https://doi.org/10.1007/s00211-003-0467-8
State	Published - Nov 2003
Externally published	Yes

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/s00211-003-0467-8

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abstract = "A variational principle, inspired by optimal control, yields a simple derivation of an error representation, global error = Σ 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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AB - A variational principle, inspired by optimal control, yields a simple derivation of an error representation, global error = Σ 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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A variational principle for adaptive approximation of ordinary differential equations

Abstract

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