The a Priori and a Posteriori Error Estimates for Modified Interior Transmission Eigenvalue Problem in Inverse Scattering (Communications in Computational Physics, 2023)
In this paper, we discuss the conforming finite element method for a modified interior transmission eigenvalues problem. We present a complete theoreticalanalysis 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 estimatorsfor eigenvalues. Finally, we report numerical experiments to show that our posteriorierror estimator is effective and the approximations can reach the optimal convergenceorder. The numerical results also indicate that the conforming finite element eigenvalues approximate the exact ones from below, and there exists a monotonic relationshipbetween the conforming finite element eigenvalues and the refractive index throughnumerical experiments.
Keywords: Modified interior transmission eigenvalues; a priori error estimates; a posteriori error estimates; adaptive algorithm.