Computation of Morse decompositions for semilinear elliptic PDEs

Smiley, Michael W.; Chun, Changbum

doi:10.1002/num.7

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Cited by 5 publications

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“…[15]) in which knowledge of only the first few eigenfunctions was assumed. In a subsequent paper [16], we will establish further error estimates on the integral and the derivatives of B(ω, λ), and describe a method for determining all solutions of (1.1)-(1.2) and their Morse indices. Together this article and [16] present a numerical method for treating the global problem of describing S(λ) and its Morse decomposition.…”

Section: Introductionmentioning

confidence: 99%

Approximation of the bifurcation function for elliptic boundary value problems

Smiley

Chun

2000

Numer. Methods Partial Differential Eq.

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The bifurcation function for an elliptic boundary value problem is a vector field B(ω) on R d whose zeros are in a one-to-one correspondence with the solutions of the boundary value problem. Finite element approximations of the boundary value problem are shown to give rise to an approximate bifurcation function B h (ω), which is also a vector field on R d . Estimates of the difference B(ω) − B h (ω) are derived, and methods for computing B h (ω) are discussed.

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Section: Introductionmentioning

confidence: 99%