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

International audienceWe 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