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An \(h\)-adaptive method in the generalized finite differences. (English) Zbl 1024.65099
Summary: This paper describes an \(h\)-adaptive method in generalized finite difference (GFD) to solve second-order partial differential equations. These equations representing the behaviour of many physical processes. The explicit difference formulae obtained make it possible to propose an a posteriori error indicator which serves as starting point for an \(h\)-adaptive method to improve the solution by selectively adding nodes to the domain.
This paper also analyses the influence of key parameters, as the number of nodes to add in each step or the minimum distance between nodes, through the analysis of the obtained solutions for different types of differential equations.

MSC:
65N06 Finite difference methods for boundary value problems involving PDEs
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74S20 Finite difference methods applied to problems in solid mechanics
35G15 Boundary value problems for linear higher-order PDEs
65N15 Error bounds for boundary value problems involving PDEs
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