Explicit Eigenvalue Bounds for Various Differential Operators

This chapter extends the theorem in Chap. 3 and applies it, in conjunction with the conforming and non-conforming finite element methods, to several traditional model eigenvalue problems involving the Laplace, the biharmonic, the Stokes, and the Steklov differential operators. For each problem, the Galerkin projection error constant \(C_h\) is evaluated explicitly to obtain lower eigenvalue bounds.