Computable error bounds for some simple dimensionally reduced models on thin domains

Mark Ainsworth, Mark E. Arnold

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

An approach is presented for deriving computable bounds on the error incurred in approximating an elliptic boundary value problem posed on a thin domain of laminated construction by a dimensionally reduced elliptic boundary value problem posed on the mid-surface. The theory includes cases where the domain is described in Cartesian or polar coordinates. Explicit upper bounds on the error are presented for flat plates, circular arches and spherical shells. The tightness of the bounds is illustrated by comparison with the true error for some representative examples.
Original languageEnglish
Pages (from-to)81-105
Number of pages24
JournalIMA Journal of Numerical Analysis
Volume21
Issue number1
DOIs
Publication statusPublished - 2001

Keywords

  • computable bounds
  • error
  • domain

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