• Media type: E-Book
  • Title: Neumann-Neumann methods for a DG discretization of elliptic problems with discontinous coefficients on geometrically nonconforming substructures
  • Contributor: Dryja, Maksymilian [Author]; Galvis, Juan [Author]; Sarkis, Marcus [Author]
  • imprint: Rio de Janeiro: IMPA, 2009
  • Published in: Instituto de Matemática Pura e Aplicada: Pré-publicações / A ; 634
  • Extent: Online-Ressource (32 S., 452 KB)
  • Language: English
  • Keywords: Forschungsbericht
  • Origination:
  • Footnote:
  • Description: discontinuous Galerkin discretization for second order elliptic equations with discontinuous coefficients in 2-D is considered. The domain of interest is assumed to be a union of polygonal substructures i of size O(Hi). We allow this substructure decomposition to be geometrically nonconforming. Inside each substructure i, a conforming finite element space associated to a triangulation Thi( i) is introduced. To handle the nonmatching meshes across i, a discontinuous Galerkin discretization is considered. In this paper additive and hybrid Neumann-Neumann Schwarz methods are designed and analyzed. Under natural assumptions on the coefficients and on the mesh sizes across @ i, a condition number estimate C(1 + maxi log Hi hi)2 is established with C independent of hi, Hi, hi/hj , and the jumps of the coefficients. The method is well suited for parallel computations and can be straightforwardly extended to three dimensional problems. Numerical results are included.
  • Access State: Open Access