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Numerical solution of partial differential equations on curved domains by collocation. (English) Zbl 0780.65069
The finite element collocation method is an efficient and highly accurate numerical method on rectangular domains. Its accuracy largely depends on the position of the collocation points. Here a method for nonrectangular domains is proposed which uses bicubic Hermite polynomials as basis functions. The rectangular domain is mapping onto the nonrectangular domain by a bilinear blended map.

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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