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An adaptive C0IPG method for the Helmholtz transmission eigenvalue problem

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Abstract

The interior penalty methods using C0 Lagrange elements (C0IPG) developed in the recent decade for the fourth order problems are an interesting topic in academia at present. In this paper, we discuss the adaptive fashion of C0IPG method for the Helmholtz transmission eigenvalue problem. We give the a posteriori error indicators for primal and dual eigenfunctions, and prove their reliability and efficiency. We also give the a posteriori error indicator for eigenvalues and design a C0IPG adaptive algorithm. Numerical experiments show that this algorithm is efficient and can get the optimal convergence rate.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11561014). The authors thank the referees for their valuable comments and suggestions that led to the large improvement of this paper.

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  1. School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550001, China

    Hao Li & Yidu Yang

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  1. Hao Li
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  2. Yidu Yang
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Correspondence to Yidu Yang.

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Li, H., Yang, Y. An adaptive C0IPG method for the Helmholtz transmission eigenvalue problem. Sci. China Math. 61, 1519–1542 (2018). https://doi.org/10.1007/s11425-017-9334-9

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