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Approximation of double bifurcation points for nonlinear eigenvalue problems. (English) Zbl 0571.65048

The mathematics of finite elements and applications IV, MAFELAP 1981, Proc. Conf., Uxbridge/Middlesex 1981, 453-461 (1982).
[For the entire collection see Zbl 0496.00017.]
A nonlinear eigenvalue problem \(u=TG(\lambda,u)\) is approximated by a family \(u_ h=T_ hG(\lambda,u_ h)\) of finite dimensional problems in the spirit of the papers of Brezzi, Rappaz and Raviart. Here, the interest is centered on double bifurcation points. It is shown how bifurcating branches are approximated by the finite dimensional solutions.
Reviewer: K.Georg

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs

Citations:

Zbl 0496.00017