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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.

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