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Two-Level Methods: The h-Version

In: Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods

Author

Listed:
  • Ernst P. Stephan

    (Leibniz University Hannover)

  • Thanh Tran

    (The University of New South Wales)

Abstract

This chapter designs and analyses non-overlapping and overlapping additive and multiplicative Schwarz methods for the h-version. The novelty of this chapter is that in order to prove the coercivity of the decomposition, a new inequality involving the global and local fractional-order Sobolev norms is used. This new development by the authors fixes an error ubiquitously seen in the literature.

Suggested Citation

  • Ernst P. Stephan & Thanh Tran, 2021. "Two-Level Methods: The h-Version," Springer Books, in: Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, chapter 0, pages 73-98, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-79283-1_3
    DOI: 10.1007/978-3-030-79283-1_3
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