Certified Real-Time Solution of Parametrized Partial Differential Equations

Ngoc Cuong Nguyen, Karen Veroy, Anthony T. Patera

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

Abstract

Engineering analysis requires the prediction of (say, a single) selected “output” se relevant to ultimate component and system performance:* typical outputs include energies and forces, critical stresses or strains, flowrates or pressure drops, and various local and global measures of concentration, temperature, and flux. These outputs are functions of system parameters, or “inputs”, μ, that serve to identify a particular realization or configuration of the component or system: these inputs typically reflect geometry, properties, and boundary conditions and loads; we shall assume that μ is a P-vector (or P-tuple) of parameters in a prescribed closed input domain D ⊂ ℝp. The input-output relationship se(μ): D → ℝ thus encapsulates the behavior relevant to the desired engineering context.
Original languageEnglish
Title of host publicationHandbook of Materials Modeling
EditorsS. Yip
PublisherSpringer
Pages1529-1564
Number of pages35
ISBN (Electronic)9781402032868
ISBN (Print)9781402032875
Publication statusPublished - 2005
Externally publishedYes

Keywords

  • Posteriori Error
  • Posteriori Error Estimation
  • Posteriori Error Estimator
  • Dual Norm
  • Reduce Basis Method

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