The Discrete Steklov-Poincaré Operator Using Algebraic Dual Polynomials

Yi Zhang; Varun Jain; Artur Palha; Marc Gerritsma

doi:10.1515/cmam-2018-0208

The Discrete Steklov-Poincaré Operator Using Algebraic Dual Polynomials

Yi Zhang^*, Varun Jain, Artur Palha, Marc Gerritsma

^*Corresponding author for this work

Aerodynamics

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6 Citations (Scopus)

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

Original language	English
Pages (from-to)	645-661
Journal	Computational Methods in Applied Mathematics
Volume	19
Issue number	3
DOIs	https://doi.org/10.1515/cmam-2018-0208
Publication status	Published - 2019

Keywords

Dual Approximation in Trace Spaces
Hybrid Finite Element Method
Spectral Elements,Domain Decomposition
Steklov-Poincaré Operator

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10.1515/cmam-2018-0208

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abstract = "In this paper, we will use algebraic dual polynomials to set up a discrete Steklov-Poincar{\'e} 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 {H^{1/2}} -norm will be shown.",

keywords = "Dual Approximation in Trace Spaces, Hybrid Finite Element Method, Spectral Elements,Domain Decomposition, Steklov-Poincar{\'e} Operator",

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AU - Palha, Artur

AU - Gerritsma, Marc

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N2 - 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 {H^{1/2}} -norm will be shown.

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

KW - Dual Approximation in Trace Spaces

KW - Hybrid Finite Element Method

KW - Spectral Elements,Domain Decomposition

KW - Steklov-Poincaré Operator

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The Discrete Steklov-Poincaré Operator Using Algebraic Dual Polynomials

Abstract

Keywords

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Mimetic Spectral Element Method and Extensions toward Higher Computational Efficiency

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