Two-grid Method And Adaptive Method For A Class Of Maxwell Eigenvalue Problem

In this paper, we construct a class of two-grid accelerating method forMaxwell eigenvalue problem and design a posteriori error estimator for theadaptive edge finite element method. The main contents of this dissertationare divided into two parts.In the first part, we first construct a two-grid acceleration algorithmthat use a coarse space to solve the generalized eigenvalue of matrix and thenuse a refine space to solve a corresponding indefinite problem. Comparingwith the generalized eigenvalue problem, we needn't solve the eigenvalueproblem in the refine space many times, so it save much computational e?ortwhile maintaining a high accuracy. In the following, we construct a modifiedtwo-grid method in order to ensure that the finite solution is the discretedivergence free.In the second part, we design a posteriori error estimator for the adaptiveedge finite element method. Comparing with a posteriori error estimatorinvolved in the adaptive inverse iteration, the new posteriori error estimator isindependent of the concrete algorithm(for example: splitting procedure), andits calculations are much simpler. Numerical experiments indicate that theadaptive meshes and the associated numerical complexity are quasi-optimal.