Toward error estimates for general space-time discretizations of the advection equation

We develop new error estimates for the one-dimensional advection equation, considering general space-time discretization schemes based on Runge–Kutta methods and finite difference discretizations. We then derive conditions on the number of points per wavelength for a given error tolerance from these...

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Bibliographic Details
Published inComputing and visualization in science Vol. 23; no. 1-4
Main Authors Gander, Martin J., Lunet, Thibaut
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2020
Springer Nature B.V
Subjects
Advection
Algorithms
Calculus of Variations and Optimal Control; Optimization
Computational Mathematics and Numerical Analysis
Computer Applications in Chemistry
Discretization
Error analysis
Estimates
Finite difference method
Mathematics
Mathematics and Statistics
Numerical Analysis
PinT 2019
Runge-Kutta method
Spacetime
Visualization
Parareal
Error estimates
Advection equation
Space-time discretization
Parallel-in-time integration
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Summary:We develop new error estimates for the one-dimensional advection equation, considering general space-time discretization schemes based on Runge–Kutta methods and finite difference discretizations. We then derive conditions on the number of points per wavelength for a given error tolerance from these new estimates. Our analysis also shows the existence of synergistic space-time discretization methods that permit to gain one order of accuracy at a given CFL number. Our new error estimates can be used to analyze the choice of space-time discretizations considered when testing Parallel-in-Time methods.
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ISSN:1432-9360
1433-0369
DOI:10.1007/s00791-020-00328-z