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hp Finite Element Approximations on Non-Matching Grids for the Stokes Problem

by L. Filippini and A. Toselli

(Report number 2002-22)

Abstract
We propose and analyze a domain decomposition method on non-matching grids for hp-finite element approximations of the Stokes problem in two dimensions. No weak or strong continuity of the discrete velocities, is imposed across the boundaries of the subdomains. Instead, we employ suitable bilinear forms defined on the common interfaces, typical of discontinuous Galerkin approximations. Our main result is the divergence stability of some finite element approximations on geometrically conforming and non-conforming subdomain partitions. Our lower bound for the inf-sup constant depends on the stability constants of the local problems and the subdomain partition. Our bounds show a slight degradation with the polynomial degree for non-conforming partitions.

Keywords: mixed problems, hp-Finite Element Method, non-matching grids, discontinuous Galerkin approximations

@Techreport{FT02_308,
  author = {L. Filippini and A. Toselli},
  title = {hp Finite Element Approximations on Non-Matching Grids for the Stokes Problem},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2002-22},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2002/2002-22.pdf },
  year = {2002}
}

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