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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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[1] Babuska, I.; Szabo, I.; Katz, B.A., The p-version of the finite element method, SIAM J. numer. anal., 18, 512-545, (1981) · Zbl 0487.65059
[2] Babuska, I., The p and h – p versions of the finite element method, Tech. note BN-1156, (1986), Inst. for Physical Science and Technology, Univ. of Maryland, The State of the Art · Zbl 0614.65089
[3] Canuto, C.; Hussaini, H.Y.; Quarteroni, A.; Zang, T.A., Spectral methods in fluid dynamics, Springer ser. comput. phys., (1988), Springer-Verlag New York · Zbl 0658.76001
[4] Funaro, D., A multidomain partial differential equations spectral approximation of elliptic equations, Numer. methods, 2, 187-205, (1986) · Zbl 0622.65104
[5] Funaro, D.; Quarteroni, A.; Zanolli, P., An iterative procedure with interface relaxation for domain decomposition methods, SIAM J. numer. anal., 25, 1213-1236, (1988) · Zbl 0678.65082
[6] Gottlieb, D.; Orszag, S.A., Numerical analysis of spectral methods: theory and apllications, CBMS regional conf. ser. in appl. math., SIAM, (1977)
[7] Engles, H., Numerical quadrature and cubature, (1980), Academic London
[8] Quarteroni, A.; Sacchi-Landriani, G., Domain decomposition preconditioners for the spectral collocation method, J. sci. comput., 3, 1, 46-75, (1988) · Zbl 0675.65116
[9] Stroud, A.H., Approximate calculation of multiple integrals, Prentice-Hall ser. automat. comput., (1971), Prentice-Hall · Zbl 0379.65013
[10] Zanolli, P., Domain decomposition algorithms for spectral methods, Calcolo, 24, 201-240, (1987) · Zbl 0649.65064
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