A New Error Bound for Reduced Basis Approximation of Parabolic Partial Differential Equations

Abstract

We consider a space-time variational formulation for linear parabolic partial differential equations. We introduce an associated Petrov-Galerkin truth finite element discretization with favorable discrete inf-sup constant beta delta: beta delta is unity for the heat equation; beta delta grows only linearly in time for non-coercive (but asymptotically stable) convection operators. The latter in turn permits effective long-time a posteriori error bounds for reduced basis approximations in sharp contrast to classical (pessimistic) exponentially growing energy estimates.

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Document Details

Document Type
Technical Report
Publication Date
Jan 26, 2012
Accession Number
ADA557547

Entities

People

  • Anthony T. Patera
  • Karsten Urban

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Computations
  • Continuity
  • Convection
  • Differential Equations
  • Eigenvalues
  • Engineering
  • Equations
  • Formulas (Mathematics)
  • Hilbert Space
  • Information Operations
  • Mathematical Analysis
  • Mathematics
  • Mechanical Engineering
  • Partial Differential Equations
  • Real Variables
  • Standards

Fields of Study

  • Mathematics

Readers

  • Economics
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

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  • Space