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Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning. (English) Zbl 0585.65073

The authors consider a two-dimensional PDE of second order with mixed homogeneous boundary conditions. They assume the uniform ellipticity of this problem. The Chebyshev pseudospectral approach is in fact an example of the weighted residual methods corresponding to orthogonal collocation. The solution of the problem is represented by finite expansions in terms of Chebyshev polynomials.
The pseudospectral method enforces the PDE to be satisfied at the internal nodes of a Gauss-Chebyshev-Lobatto quadrature rule. Various numerical results are presented and compared for several problems on square and L-shaped regions using some finite elements (Lagrange bilinear, biquadratic and Hermite bicubic).
Reviewer: C.-I.Gheorghiu

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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