Local and Parallel Finite Element Algorithms for the Transmission Eigenvalue Problem

Based on the work of Xu and Zhou (Math Comp 69:881–909, 2000), we establish local and parallel algorithms for the Helmholtz transmission eigenvalue problem. For the $$H^2$$H2-conforming finite element and the spectral element approximations, we prove the local error estimates and the efficiency of local and parallel algorithms. Numerical experiments indicate that our algorithms are easy to implement on the existing packages, and can be used to solve the transmission eigenvalue problem with local low smooth eigenfunctions efficiently.

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