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Pseudospectral approximation of a PDE defined on a triangle. (English) Zbl 0728.65092
The author proposes to spectrally approximate the solution to a partial differential equation defined on a triangle T by the following method: Using the barycenter of T as “fourth” corner, subdivide T into four quadrangles \(T_ i\), transform each \(T_ i\) into a square \(Q_ i\) by a smooth mapping, and then discretize the transformed equation on the \(Q_ i\) by a collocation multidomain procedure.
Numerical results obtained by this method for a model Poisson equation defined on an equilateral triangle and subject to homogeneous Dirichlet boundary conditions are presented.

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
Full Text: DOI
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