Bifurcation Indicator Based on Meshless and Asymptotic Numerical Methods for Nonlinear Poisson Problems - Université de Lorraine Access content directly
Journal Articles Numerical Methods for Partial Differential Equations Year : 2014

Bifurcation Indicator Based on Meshless and Asymptotic Numerical Methods for Nonlinear Poisson Problems

Abstract

We propose in this work new algorithms associating asymptotic numerical method and meshless discretization (MFS-MPS: Method of fundamental solutions-Method of particular solutions) to compute branch solutions of nonlinear Poisson problems. To detect singular points on these branches, geometrical indicator, Pade approximants, and analytical bifurcation indicator are proposed. Numerical applications show the robustness and the effectiveness of the proposed algorithms.

Dates and versions

hal-01503448 , version 1 (07-04-2017)

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Cite

Abdeljalil Tri, Hamid Zahrouni, Michel Potier-Ferry. Bifurcation Indicator Based on Meshless and Asymptotic Numerical Methods for Nonlinear Poisson Problems. Numerical Methods for Partial Differential Equations, 2014, 30 (3), pp.978-993. ⟨10.1002/num.21851⟩. ⟨hal-01503448⟩
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