Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form

TL;DR

This paper proves that h-adaptive mixed finite element methods achieve optimal convergence rates for eigenvalue clusters of the Laplace operator, applicable in 2D and 3D with common mixed spaces.

Contribution

It establishes the optimal convergence of adaptive mixed FEM for eigenvalue clusters in the Laplace problem, extending results to Raviart-Thomas and BDM spaces with fixed polynomial degree.

Findings

Optimal convergence rates proven for adaptive mixed FEM

Results valid for Raviart-Thomas and BDM spaces

Applicable in both 2D and 3D settings

Abstract

It is shown that the h-adaptive mixed finite element method for the discretization of eigenvalue clusters of the Laplace operator produces optimal convergence rates in terms of nonlinear approximation classes. The results are valid for the typical mixed spaces of Raviart-Thomas or Brezzi-Douglas-Marini type with arbitrary fixed polynomial degree in two and three space dimensions.