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Stable enrichment and local preconditioning in the particle-partition of unity method. (English) Zbl 1217.65210

The author studies the stability and approximation properties of enriched meshfree and generalized finite element methods. He focuses on the particle-partition of unity method, but the presented results hold for any partition of unity based enrichment scheme. Error bounds are discussed and numerical examples are also provided.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65F08 Preconditioners for iterative methods
35J25 Boundary value problems for second-order elliptic equations

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References:

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