The Raviart-Thomas Mixed Finite Element Method for Asymmetric Second-Order Elliptic Eigenvalue Problems

This paper studies the lowest-order Raviart-Thomas mixed finite element method for a more general class of second-order elliptic eigenvalue problems, and through analysis, obtains an a priori error estimate, which is optimal with respect to the mesh sizeℎ.First, based on the uniqueness of the solution to the corresponding steady-state problem, we define the fully continuous operator and derive an abstract error estimate. Then, on this basis, we obtain error estimates for the eigenvalues and eigenfunctions. Finally, we conduct corresponding numerical experiments, and the results are consistent with the theory.