A simple low-degree optimal finite element scheme for the elastic transmission eigenvalue problem

01/26/2021

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by   Yingxia Xi, et al.

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The paper presents a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials and obtains optimal convergence rate. Compared with other low-degree and nonconforming finite element schemes, the scheme inherits the continuous bilinear form which does not need extra stabilizations and is thus simple to implement.