Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 25, No 2, (1999), 177p-184p
Abstract:
We consider a model eigenvalue problem (EVP) in 1D, with
periodic or semi–periodic boundary conditions (BCs). The discretization of
this type of EVP by consistent mass finite element methods (FEMs) leads to
the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric
matrices, with a certain (skew–)circulant structure. In this paper we fix our
attention to the use of a quadratic FE–mesh. Explicit expressions for the
eigenvalues of the resulting algebraic EVP are established. This leads to an
explicit form for the approximation error in terms of the mesh parameter,
which confirms the theoretical error estimates, obtained in [2].
