The Discrete Steklov–Poincaré Operator Using Algebraic Dual Polynomials

Yi Zhanghttp://orcid.org/https://orcid.org/0000-0003-4208-716X 1 , Varun Jain 2 , Artur Palha 3 , and Marc Gerritsma 2
  • 1 Department of Aerodynamics, Wind Energy, Flight Performance and Propulsion, Delft University of Technology, P.O. Box 5058, 2600 GB, Delft, The Netherlands
  • 2 Department of Aerodynamics, Wind Energy, Flight Performance and Propulsion, Delft University of Technology, P.O. Box 5058, 2600 GB, Delft, The Netherlands
  • 3 Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
Yi ZhangORCID iD: https://orcid.org/0000-0003-4208-716X, Varun Jain
  • Department of Aerodynamics, Wind Energy, Flight Performance and Propulsion, Delft University of Technology, P.O. Box 5058, 2600 GB, Delft, The Netherlands
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, Artur Palha
  • Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
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and Marc Gerritsma
  • Department of Aerodynamics, Wind Energy, Flight Performance and Propulsion, Delft University of Technology, P.O. Box 5058, 2600 GB, Delft, The Netherlands
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Abstract

In this paper, we will use algebraic dual polynomials to set up a discrete Steklov–Poincaré operator for the mixed formulation of the Poisson problem. The method will be applied in curvilinear coordinates and to a test problem which contains a singularity. Exponential convergence of the trace variable in H1/2-norm will be shown.

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