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Constrained Mountain Pass Algorithm for the Numerical Solution of Semilinear Elliptic Problems

In: Numerical Mathematics and Advanced Applications

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  • Jiří Horák

    (University of Basel, Department of Mathematics)

Abstract

Summary A new numerical algorithm for solving semilinear elliptic problems is presented. A variational formulation is used and critical points of a C 1-functional subject to a constraint given by a level set of another C 1-functional (or an intersection of such level sets of finitely many functionals) are sought. First, constrained local minima are looked for, then constrained mountain pass points. The approach is based on the mountain pass theorem in a constrained setting.

Suggested Citation

  • Jiří Horák, 2004. "Constrained Mountain Pass Algorithm for the Numerical Solution of Semilinear Elliptic Problems," Springer Books, in: Miloslav Feistauer & Vít Dolejší & Petr Knobloch & Karel Najzar (ed.), Numerical Mathematics and Advanced Applications, pages 449-458, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18775-9_42
    DOI: 10.1007/978-3-642-18775-9_42
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