Ivanenko, S. A. Existence of equations describing the classes of nondegenerate curvilinear coordinates in arbitrary domains. (Russian, English) Zbl 1173.35417 Zh. Vychisl. Mat. Mat. Fiz. 42, No. 1, 47-52 (2002); translation in Comput. Math. Math. Phys. 42, No. 1, 43-48 (2002). Curvilinear coordinates in the simple connectedness domain are constructed by virtue of mapping of the unit square onto this domain. There is formulated a concept, which enables to identify classes of bijective mappings. A functional is derived, which depends upon derivative of desired functions and upon variable coefficients. These coefficients are elements of certain symmetric and positive definite matrix. There is formulated a discrete analog of variational concept. Reviewer: Andrei Zemskov (Moskva) Cited in 1 Document MSC: 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 58E30 Variational principles in infinite-dimensional spaces Keywords:numerical grids; variational methods; functional; optimality; Laplace equations; Euler equation PDFBibTeX XMLCite \textit{S. A. Ivanenko}, Zh. Vychisl. Mat. Mat. Fiz. 42, No. 1, 47--52 (2002; Zbl 1173.35417); translation in Comput. Math. Math. Phys. 42, No. 1, 43--48 (2002)