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[02647] Poincaré operators for BGG complexes

  • Session Time & Room : 5D (Aug.25, 15:30-17:10) @F402
  • Type : Contributed Talk
  • Abstract : Poincaré integral operators give explicit potential and provide an inverse of differential operators in the sense of null-homotopy. These operators play a key role in the mathematical and numerical analysis of fluid and electromagnetic problems. Consequences include the well-posedness of the Stokes problem and the p-robustness of high-order finite element methods. In this talk, we derive such operators for the Bernstein-Gelfand-Gelfand (BGG) complexes with potential applications in elasticity and relativity. The idea is to carry over the results for the de-Rham complex by Costabel and McIntosh to these cases by homological algebra.
  • Classification : 58J10, 35N05, 58A12, 58A14, 65N30, finite element methods, Hilbert complexes, Bernstein-Gelfand-Gelfand construction, applied analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Andreas Čap (University of Vienna)
    • Kaibo Hu (University of Oxford)