Application of essential boundary conditions in mesh-free methods: A corrected collocation method.

*(English)*Zbl 0965.76069Summary: Collocation methods for applying essential boundary conditions are defined as those methods in which conditions are enforced exactly at a discrete set of boundary nodes. In mesh-free methods, this is usually accomplished by replacing rows of the matrix equations which result from discretization of the weak form with equations which ensure the enforcement of boundary conditions. In this paper, an inconsistency in this method is pointed out, and a correction is proposed. Numerical tests are done on one- and two-dimensional equations; it is shown that convergence rates decrease with the use of the invalid traditional collocation, and are restored with the corrected method.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76R99 | Diffusion and convection |

##### Keywords:

corrected collocation method; one-dimensional advection-diffusion equation; two-dimensional Laplace equation; mesh-free methods; boundary conditions; convergence rates
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\textit{G. J. Wagner} and \textit{W. K. Liu}, Int. J. Numer. Methods Eng. 47, No. 8, 1367--1379 (2000; Zbl 0965.76069)

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