Convergence of the Finite Element Method Applied to the Eigenvalue Problem $Δu + λu = 0$
Kazuo Ishihara · Publications of the Research Institute for Mathematical Sciences · 1977
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