Convergence of the Finite Element Method Applied to the Eigenvalue Problem $Δu + λu = 0$ | Zendy

Kazuo Ishihara | Zendy

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Convergence of the Finite Element Method Applied to the Eigenvalue Problem $Δu + λu = 0$

Author(s) -

Kazuo Ishihara

Publication year - 1977

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195190100

Subject(s) - mathematics , eigenvalues and eigenvectors , finite element method , bounded function , mathematical analysis , domain (mathematical analysis) , convergence (economics) , piecewise , boundary (topology) , dirichlet boundary condition , type (biology) , neumann boundary condition , laplace operator , physics , ecology , quantum mechanics , biology , economics , thermodynamics , economic growth

This paper is concerned with the finite element approximation schemes for the eigenvalue problem: (1) Au + fai = Q in £ with the boundary condition « = 0 on S (Dirichlet type) or du/dn — Q on S (Neumann type) where A is the Laplacian, J2 is a bounded domain in R, S is the piecewise smooth boundary of J2, and n is the exterior normal. We put the equation (1) into the weak form: (2) a (u, v) — I (u, v) for any v^V where

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