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Dual-Primal FETI algorithms for edge element approximations: Two-dimensional h and p finite elements on shape-regular meshes

by A. Toselli and X. Vasseur

(Report number 2004-01)

Abstract
A family of dual-primal FETI methods for edge element approximations in two dimensions is proposed and analyzed. The primal constraints are here averages over subdomain edges. It is shown that the condition number of the corresponding method is independent of the number of substructures and grows only polylogarithmically with the number of unknowns associated with individual substructures. The estimate is also independent of the jumps of both of the coefficients of the original problem. Numerical results validating our theoretical bounds are given.

Keywords: Edge elements, Maxwell's equations, finite elements, spectral elements, domain decomposition, FETI, preconditioners, heterogeneous coefficients

@Techreport{TV04_329,
  author = {A. Toselli and X. Vasseur},
  title = {Dual-Primal FETI algorithms for edge element approximations: Two-dimensional h and p finite elements on shape-regular meshes},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2004-01},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2004/2004-01.pdf },
  year = {2004}
}

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