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

作     者：Hao Li Yidu Yang 

作者机构：School of Mathematical Sciences Guizhou Normal University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2018年第61卷第8期

页      面：1519-1542页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11561014) 

主　　题：transmission eigenvalues interior penalty Galerkin method Lagrange elements a posteriori error estimates adaptive algorithm 

摘      要：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 at present. In this paper, we discuss the adaptive proporty 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.