A Laplace transform certified reduced basis method; application to the heat equation and wave equation

DOI10.1016/j.crma.2011.02.003zbMath1215.65156OpenAlexW1983528929MaRDI QIDQ533974

D. B. Phuong Huynh, David J. Knezevic, Anthony T. Patera

Publication date: 10 May 2011

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1721.1/99386

zbMATH Keywords

Laplace transformnumerical resultsheat equationwave equationerror boundinverse Laplace transformreduced basis methodeigenfunction decompositionOffline-Online decomposition

Mathematics Subject Classification ID

Heat equation (35K05) Wave equation (35L05) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Laplace transform (44A10) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Boundary element methods for initial value and initial-boundary value problems involving PDEs (65M38)

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Cites Work

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• Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
• Estimation of the Error in the Reduced Basis Method Solution of Nonlinear Equations
• Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems
• Reduced basis method for finite volume approximations of parametrized linear evolution equations
• Introduction to Finite Element Vibration Analysis

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