Abstract
We investigate Fourier collocation approximations of the evolutionary twodimensional Burgers equation. The numerical schemes are not required to be semi-conservative. We obtain stability estimates in theH 1(Ω) norm that are uniform in time. Our results show that collocation techniques do not yield instability, at least if the resolution is fine enough.
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Marion, M. On the stability of collocation methods for the two-dimensional Burgers equation — The Fourier case. J Sci Comput 9, 405–417 (1994). https://doi.org/10.1007/BF01575100
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DOI: https://doi.org/10.1007/BF01575100