Meshless Galerkin methods using radial basis functions. (English) Zbl 1020.65084

Summary: We combine the theory of radial basis functions with the field of Galerkin methods to solve partial differential equations (PDE). After a general description of the method we show convergence and derive error estimates for smooth problems in arbitrary dimensions. We restrict ourselves to second-order PDE, but a generalization to higher-order equations can be done in an obvious way.


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
41A30 Approximation by other special function classes
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