Application of triangular differential quadrature to problems with curved boundaries. (English) Zbl 1010.65047
In order to approximate elliptic boundary value problems set on curved boundary domains, the author extends his triangular differential quadrature method to curvilinear triangles.
For that, he uses a suitable geometric transformation from a straight sides reference triangle to an arbitrary curvilinear triangle. This transformation is clearly explicited and its accuracy and its relevance are illustrated by the numerical solution of a Poisson problem set on a circular domain.
For that, he uses a suitable geometric transformation from a straight sides reference triangle to an arbitrary curvilinear triangle. This transformation is clearly explicited and its accuracy and its relevance are illustrated by the numerical solution of a Poisson problem set on a circular domain.
Reviewer: Michel Bernadou (Paris La Defense)
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
Keywords:
triangular differential quadrature method; weighting coefficients; Poisson equation; numerical example; curved boundaryReferences:
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