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# Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Volume 19, Issue 3

# The Discrete Steklov–Poincaré Operator Using Algebraic Dual Polynomials

Yi Zhang
/ 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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• Other articles by this author:
/ Artur Palha
• Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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• Other articles by this author:
/ 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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• Other articles by this author:
Published Online: 2019-05-07 | DOI: https://doi.org/10.1515/cmam-2018-0208

## 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 ${H}^{1/2}$-norm will be shown.

MSC 2010: 65N30; 65N35; 76M10; 76M25

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Accepted: 2019-03-05

Published Online: 2019-05-07

Published in Print: 2019-07-01

Citation Information: Computational Methods in Applied Mathematics, Volume 19, Issue 3, Pages 645–661, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840,

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