Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form
arXiv:1504.06418
Originality Synthesis-oriented
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Provides theoretical justification for adaptive methods in eigenvalue problems, benefiting numerical analysts and engineers solving PDE eigenvalue problems.
The paper proves that h-adaptive mixed FEM achieves optimal convergence rates for eigenvalue clusters of the Laplace operator, using standard mixed spaces in 2D and 3D.
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.