On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains

There exists a growing literature on using the Fokas method (unified transform method) to solve Laplace and Helmholtz problems on convex polygonal domains. We show here that the convexity requirement can be eliminated by the use of a ‘virtual side’ concept, thereby significantly increasing the flexi...

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Veröffentlicht in:	Journal of computational physics 2018-12, Vol.374, p.996-1016
Hauptverfasser:	Colbrook, Matthew J., Flyer, Natasha, Fornberg, Bengt
Format:	Artikel
Sprache:	eng
Schlagworte:	Boundary value problems Computational physics Convergence Convexity Corner singularities Domains Elliptic PDEs Fokas method/uniform transform method Helmholtz equations Laplace transforms Mathematical analysis Singularities
Online-Zugang:	Volltext
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