TY - JOUR
T1 - The a Priori and a Posteriori Error Estimates for Modified Interior Transmission Eigenvalue Problem in Inverse Scattering
AU - Li , Yanjun
AU - Yang , Yidu
AU - Bi , Hai
JO - Communications in Computational Physics
VL - 2
SP - 503
EP - 529
PY - 2023
DA - 2023/09
SN - 34
DO - http://doi.org/10.4208/cicp.OA-2023-0124
UR - https://global-sci.org/intro/article_detail/cicp/21976.html
KW - Modified interior transmission eigenvalues, a priori error estimates, a posteriori error estimates, adaptive algorithm.
AB - <p style="text-align: justify;">In this paper, we discuss the conforming finite element method for a modified interior transmission eigenvalues problem. We present a complete theoretical
analysis for the method, including the a priori and a posteriori error estimates. The theoretical analysis is conducted under the assumption of low regularity on the solution.
We prove the reliability and efficiency of the a posteriori error estimators for eigenfunctions up to higher order terms, and we also analyze the reliability of estimators
for eigenvalues. Finally, we report numerical experiments to show that our posteriori
error estimator is effective and the approximations can reach the optimal convergence
order. The numerical results also indicate that the conforming finite element eigenvalues approximate the exact ones from below, and there exists a monotonic relationship
between the conforming finite element eigenvalues and the refractive index through
numerical experiments.</p>