This is the 1-D convection-diffusion operator eu'' + u' on [0,1] with u(0)=u(1)=0 for e=1/30, discretised using a Chebyshev spectral method [1]. The boundaries of pseudospectra of the infinite dimensional operator are shaped approximately like parabolas, as already revealed on the right part of this low-dimensional approximation [2].
[1]: L. N. Trefethen, "Spectral methods in MATLAB", SIAM, 2000.
[2]: S. C. Reddy and L. N. Trefethen, "Pseudospectra of the convection-diffusion operator", SIAM J. Appl. Math. 54(6), pp. 1634-1649, 1994.
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