Abstract
About 25 years ago Wasow and Lehman got an asymptotic series for a harmonic function in a sector. This showed that, in various important cases, the first derivative of the function becomes infinite as one approaches the vertex of the sector. For this reason, finite difference or finite element methods of a fixed mesh give poor accuracy near the vertex. The asymptotic series of Wasow and Lehman cannot be used for calculations near the vertex since the derivations of the series gave no means to compute the numerical values of the coefficients of the series.
In this talk means are provided for computing the numerical values of the coefficients. Moreover, by suitably pairing some terms of the series, the resulting series of terms and pairs turns out to be convergent. It is therefore quite suitable for calculating values of the harmonic function near the vertex.
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© 1985 Springer-Verlag
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Rosser, J.B. (1985). Calculation of potential in a sector. In: Grisvard, P., Wendland, W.L., Whiteman, J.R. (eds) Singularities and Constructive Methods for Their Treatment. Lecture Notes in Mathematics, vol 1121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076274
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DOI: https://doi.org/10.1007/BFb0076274
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15219-4
Online ISBN: 978-3-540-39377-1
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