Eigenvalue approximation by mixed non-conforming finite element methods
A theory for the approximation of eigenvalue problems in mixed form by non-conforming methods is given. The paper is organized as follows. Section 1 is an introduction. In Section 2, the statement of the eigenvalue problem is given. In Section 3, a set of sufficient conditions for having good convergence properties for the approximation of the eigenvalue/eigenvector pairs in the sense that the numerical method does not introduce spurious modes are given. In Section 4, this theory is applied to analyze the problem of determining the vibrational modes of a linear elastic structure using the classical Hellinger-Reissner mixed formulation. It is shown that a numerical method based on the lowest-order Arnold-Winther non-conforming space provides a spectrally correct approximation of the eigenvalue/eigenvector pairs. Optimal-order error estimates are proved, too.
scientific article; zbMATH DE number 6418690
scientific article