A FINITE ELEMENT METHOD FOR A CURLCURL-GRADDIV EIGENVALUE INTERFACE PROBLEM

作者：Duan, Huoyuan^*; Lin, Ping^*; Tan, Roger C. E.^*

来源：SIAM Journal on Numerical Analysis, 2016, 54(2): 1193-1228.

DOI：10.1137/140980004

• generalized Maxwell eigenvalue problem of curlcurl-graddiv operator
• H-1-conforming finite element method
• piecewise non-H-1-space solution
• error estimates
• spectral correctness

In this paper we propose and study a finite element method for a curlcurl-graddiv eigenvalue interface problem. Its solution may be of piecewise non-H-1. We would like to approximate such a solution in an H-1-conforming finite element space. With the discretizations of both curl and div operators of the underlying eigenvalue problem in two finite element spaces, the proposed method is essentially a standard H-1-conforming element method, up to element bubbles which can be statically eliminated at element levels. We first analyze the proposed method for the related source interface problem by establishing the stability and the error bounds. We then analyze the underlying eigenvalue interface problem, and we obtain the error bounds O(h(2r0)) for eigenvalues which correspond to eigenfunctions in Pi(J)(j-1) (H-r(Omega(j)))(3) (sic) (H-r0 (Omega))(3) space, where the piecewise regularity r and the global regularity r(0) may belong to the most interesting interval [0, 1].

• 出版日期2016
• 单位武汉大学