An Iterative Finite Element Scheme for Bifurcation Analysis of Semi-Linear Elliptic Equations

概要

論文の詳細を見る
A finite element scheme is proposed for bifurcation analysis of semi-linear elliptic equations of two-dimensional spaces. An iteration process is employed to treat nonlinearity of the problems and to avoid numerical instability in the vicinity of bifurcation points. Convergence analysis of the iterative process and error analysis of the finite element solutions are performed by the use of the principle of contraction mappings and some established results of the finite element method. The proposed approach is also available for the analysis of initial imperfection. Numerical solutions are illustrated to see the effectiveness of the proposed method.
宇宙航空研究開発機構の論文