Rates of robust superlinear convergence of preconditioned Krylov methods for elliptic FEM problems

This paper considers the iterative solution of finite element discretizations of second-order elliptic boundary value problems. Mesh independent estimations are given for the rate of superlinear convergence of preconditioned Krylov methods, involving the connection between the convergence rate and t...

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Bibliographic Details
Published in:	Numerical algorithms Vol. 96; no. 2; pp. 719 - 738
Main Authors:	Castillo, S. J., Karátson, J.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01-06-2024 Springer Nature B.V
Subjects:	Algebra Algorithms Boundary value problems Computer Science Convergence Eigenvalues Hilbert space Iterative solution Numeric Computing Numerical Analysis Original Paper Partial differential equations Theory of Computation Finite element method Elliptic boundary value problems Preconditioned Krylov iterations Superlinear convergence
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Summary:	This paper considers the iterative solution of finite element discretizations of second-order elliptic boundary value problems. Mesh independent estimations are given for the rate of superlinear convergence of preconditioned Krylov methods, involving the connection between the convergence rate and the Lebesgue exponent of the data. Numerical examples demonstrate the theoretical results.
ISSN:	1017-1398 1572-9265
DOI:	10.1007/s11075-023-01663-1