Toward error estimates for general space-time discretizations of the advection equation
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AbstractWe 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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2003 ◽
Vol 188
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pp. 157-175
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1997 ◽
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pp. 119-134
1978 ◽
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pp. 975-981
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1987 ◽
Vol 27
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pp. 46-57
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2019 ◽
Vol 57
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pp. 1730-1756
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2005 ◽
Vol 167
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pp. 46-67
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