A new meshless method using Taylor series to solve elasticity problems
DOI:
https://doi.org/10.13052/17797179.2012.721500Keywords:
PDE, meshless method, convergence analysis, Taylor series expansion, Domb– Sykes plotAbstract
A meshless method is presented and analysed. In this approach, one discretises only the boundary, the partial differential equation being solved in the domain by using Taylor series expansion. A least square method is used to apply boundary conditions. In this paper, the method is applied to Navier equations for linear elasticity. Various tests are presented to discuss the efficiency and robustness of the method. The convergence is exponential with respect to the degree but it depends on the radius of convergence of the series. That is why an algorithm has been associated with the Domb–Sykes plot that is a classical method to detect singularities and evaluate the radius of convergence.
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