2004
DOI: 10.1016/j.jcp.2004.02.001
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Spectral collocation schemes on the unit disc

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Cited by 33 publications
(30 citation statements)
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“…Some of them have been used in polar coordinates by different authors [14,19,15,20]. They are listed in Table 1.…”
Section: Test For the Radial Meshesmentioning
confidence: 99%
See 1 more Smart Citation
“…Some of them have been used in polar coordinates by different authors [14,19,15,20]. They are listed in Table 1.…”
Section: Test For the Radial Meshesmentioning
confidence: 99%
“…A recent article [13] compares seven different radial bases for the approximation of functions and for solving the Poisson equation on the unit disk. When collocation methods are used, some authors add regularity conditions at the origin [14][15][16], while others avoid including the origin in the collocation mesh [17][18][19][20].…”
Section: Introductionmentioning
confidence: 99%
“…The mesh contains 33 elements (Figure 8) and the polynomial degree chosen is N = 6. An integration order P = 8 is chosen, see (23). De Maerschalck and Gerritsma [37] demonstrated that over-integration is beneficial for non-smooth problems to account for the slowly decaying higher-order modes in the system.…”
Section: Results For Subsonic Flowmentioning
confidence: 99%
“…A coordinate system transformation is another possible technique. Heinrichs [8] used conformal mapping to transform a Cartesian coordinate system into a polar system, and a similar approach was proposed by Hansen et al [9]. The transformation was applied to the nodes closest to the center, and the components, already in Cartesian form, were then averaged, giving as a result the value of the pole.…”
Section: Introductionmentioning
confidence: 99%