An adaptive C 0IPG method for the Helmholtz transmission eigenvalue problem

The interior penalty methods using C (0) Lagrange elements (C (0)IPG) 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 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.