A Brief Overview of the State-of-the-Practice and Current Challenges of Solution Verification

DOI10.1007/978-3-540-77362-7_10zbMath1328.65207OpenAlexW48698514MaRDI QIDQ3196290

François M. Hemez, James R. Kamm

Publication date: 29 October 2015

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-77362-7_10

zbMATH Keywords

convergencefinite elementsnumerical examplesBurgers equationconservation lawerror boundsdiscontinuous solutionssolution verificationequations-of-motion

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hyperbolic conservation laws (35L65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Algorithms with automatic result verification (65G20)

Cites Work

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• The modified equation approach to the stability and accuracy analysis of finite-difference methods
• Review of code and solution verification procedures for computational simulation
• On balanced approximations for time integration of multiple time scale systems.
• Finite Volume Methods for Hyperbolic Problems

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