Abstract
A spectral Legendre method for the advection-diffusion equation is stabilized with the addition of locally supported bubble functions. It is shown that the spectral accuracy of the scheme is preserved and its stability is increased. Several strategies for choosing the stabilization parameter are proposed and compared with the aid of numerical tests.
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Puppo, G. Bubble Stabilization of Spectral Methods: The Multidimensional Case. Journal of Scientific Computing 13, 115–149 (1998). https://doi.org/10.1023/A:1023239710075
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DOI: https://doi.org/10.1023/A:1023239710075