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The method of finite spheres. (English) Zbl 0952.65091
Steady-state elliptic boundary-value problems for ordinary or partial differential equations are solved numerically by the method of finite spheres, viewed as a special case of meshless local Petrov-Galerkin procedure. Special emphasis is payed to a numerical integration scheme, the way in which the Dirichlet boundary conditions are incorporated, and the treatment of doubly-connected domains. The illustrative one- and two-dimensional examples include a string with distributed loading, a high Peclet number flow problem, Poisson’s equation, and the linear elasticity.

MSC:
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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