Numerical Analysis of the Finite Element Method Applied to Bifurcation Problems of Turning Point Type : I. Theoretical Analysis

概要

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This paper presents theoretical numerical analysis of the finite element method applied to bifurcation problems of turning point (or limit point) type. The main tool of analysis is the implicit function theorem based on the principle of contraction mappings, by which some error estimates are obtained for the finite element solutions. Especially, we have shown that the original turning point can be well approximated by the finite element method. Numerical results will be given in the second part of this paper.
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