Convergence for Eigenvalue Problems with Mesh Adaptivity
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The main result of this paper is Theorem 3.2 below which proves convergence of the adaptive method and also demonstrates the decay of oscillations of the sequence of approximate eigenfunctions. Before proving this result we need a final lemma.
Theorem 3.2 Provided the initial mesh is chosen so that is small enough, there exists a constant such that the recursive application of Algorithm yields a convergent sequence of approximate eigenvalues and eigenvectors, with the property:
where and are positive constants.
Remark 3.3 The initial mesh convergence threshold and the constants and may depend on , and .