English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The goal of this paper is to develop numerical methods computing a fewsmallest elastic interior transmission eigenvalues, which are of practicalimportance in inverse elastic scattering theory. The problem is challengingsince it is nonlinear, nonselfadjoint, and of fourth order. In this paper, weconstruct a lowest order mixed finite element method which is close to theCiarlet-Raviart mixed finite element method. This scheme is based on Lagrangefinite elements and is one of the less expensive methods in terms of the amountof degrees of freedom. Due to the nonselfadjointness, the discretization ofelastic transmission eigenvalue problem leads to a non-classical mixed methodwhich does not fit into the framework of classical theoretical analysis. Instead, we obtain the convergence analysis based on the spectral approximationtheory of compact operators. Numerical examples are presented to verify thetheory. Both real and complex eigenvalues can be obtained.

A lowest order mixed finite element method for the elastic transmission eigenvalue problem