A two-level method for mimetic finite difference discretizations of elliptic problems

Paola F. Antonietti, Marco Verani, Ludmil Zikatanov

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We propose and analyze a two-level method for mimetic finite difference approximations of second order elliptic boundary value problems. We prove that the two-level algorithm is uniformly convergent, i.e., the number of iterations needed to achieve convergence is uniformly bounded independently of the characteristic size of the underlying partition. We also show that the resulting scheme provides a uniform preconditioner with respect to the number of degrees of freedom. Numerical results that validate the theory are also presented.

Original languageEnglish (US)
Pages (from-to)2674-2687
Number of pages14
JournalComputers and Mathematics with Applications
Volume70
Issue number11
DOIs
StatePublished - Dec 2015

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Two-level Method
Elliptic Problems
Boundary value problems
Finite Difference
Discretization
Finite Difference Approximation
Elliptic Boundary Value Problems
Preconditioner
Degree of freedom
Partition
Iteration
Numerical Results

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

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A two-level method for mimetic finite difference discretizations of elliptic problems. / Antonietti, Paola F.; Verani, Marco; Zikatanov, Ludmil.

In: Computers and Mathematics with Applications, Vol. 70, No. 11, 12.2015, p. 2674-2687.

Research output: Contribution to journalArticle

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AU - Verani, Marco

AU - Zikatanov, Ludmil

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AB - We propose and analyze a two-level method for mimetic finite difference approximations of second order elliptic boundary value problems. We prove that the two-level algorithm is uniformly convergent, i.e., the number of iterations needed to achieve convergence is uniformly bounded independently of the characteristic size of the underlying partition. We also show that the resulting scheme provides a uniform preconditioner with respect to the number of degrees of freedom. Numerical results that validate the theory are also presented.

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