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arXiv · 1708.06104

An adaptive C0IPG method for the Helmholtz transmission eigenvalue problem

Hao Li·Yidu Yang
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Abstract

The interior penalty methods using $C^0$ Lagrange elements ($C^0$IPG) developed in the last decade for the fourth order problems are an interesting topic in academia at present. In this paper, we discuss the adaptive fashion of $C^0$IPG 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 $C^0$IPG adaptive algorithm. Numerical experiments show that this algorithm is efficient and can get the optimal convergence rate.

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Hao Li, Yidu Yang. 2017-08-21. An adaptive C0IPG method for the Helmholtz transmission eigenvalue problem. https://arxiv.org/abs/1708.06104

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