scholarly journals Stable broken $H^1$ and $H(\mathrm {div})$ polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions

2019 ◽  
Vol 89 (322) ◽  
pp. 551-594 ◽  
Author(s):  
Alexandre Ern ◽  
Martin Vohralík
Keyword(s):  
Flux Reconstruction ◽  
Polynomial Degree ◽  
Three Space ◽  
Polynomial Extensions

scholarly journals A New Generalization of the P1 Non-Conforming FEM to Higher Polynomial Degrees

2017 ◽  
Vol 17 (1) ◽  
pp. 161-185 ◽  
Author(s):  
Mira Schedensack
Keyword(s):  
Adaptive Algorithm ◽  
Numerical Experiments ◽  
Convergence Rates ◽  
A Priori ◽  
Projection Property ◽  
Polynomial Degree ◽  
Poisson Problem ◽  
Optimal Convergence Rates ◽  
New Formulation ◽  
Three Space

AbstractThis paper generalizes the non-conforming FEM of Crouzeix and Raviart and its fundamental projection property by a novel mixed formulation for the Poisson problem based on the Helmholtz decomposition. The new formulation allows for ansatz spaces of arbitrary polynomial degree and its discretization coincides with the mentioned non-conforming FEM for the lowest polynomial degree. The discretization directly approximates the gradient of the solution instead of the solution itself. Besides the a priori and medius analysis, this paper proves optimal convergence rates for an adaptive algorithm for the new discretization. These are also demonstrated in numerical experiments. Furthermore, this paper focuses on extensions of this new scheme to quadrilateral meshes, mixed FEMs, and three space dimensions.

scholarly journals A flux reconstruction method for the Korteweg-de Vries equation

2021 ◽  
Vol 1978 (1) ◽  
pp. 012031
Author(s):  
Ningbo Guo ◽  
Yaming Chen ◽  
Xiaogang Deng
Keyword(s):  
Vries Equation ◽  
Flux Reconstruction ◽  
Reconstruction Method ◽  
De Vries

scholarly journals Colourful Poincaré symmetry, gravity and particle actions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Joaquim Gomis ◽  
Euihun Joung ◽  
Axel Kleinschmidt ◽  
Karapet Mkrtchyan
Keyword(s):  
Field Theory ◽  
Free Particle ◽  
Three Dimensional ◽  
Background Field ◽  
Quantum Field ◽  
Symmetry Factor ◽  
Starting Point ◽  
Poincaré Algebra ◽  
Poincaré Symmetry ◽  
Three Space

Abstract We construct a generalisation of the three-dimensional Poincaré algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincaré gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincaré symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.

scholarly journals Three-dimensional Maxwellian extended Newtonian gravity and flat limit

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Patrick Concha ◽  
Lucrezia Ravera ◽  
Evelyn Rodríguez ◽  
Gustavo Rubio
Keyword(s):  
Cosmological Constant ◽  
Three Dimensional ◽  
Expansion Method ◽  
Gravity Models ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
Relativistic Limit ◽  
Expansion Procedure ◽  
Three Space ◽  
Chern Simons

Abstract In the present work we find novel Newtonian gravity models in three space-time dimensions. We first present a Maxwellian version of the extended Newtonian gravity, which is obtained as the non-relativistic limit of a particular U(1)-enlargement of an enhanced Maxwell Chern-Simons gravity. We show that the extended Newtonian gravity appears as a particular sub-case. Then, the introduction of a cosmological constant to the Maxwellian extended Newtonian theory is also explored. To this purpose, we consider the non-relativistic limit of an enlarged symmetry. An alternative method to obtain our results is presented by applying the semigroup expansion method to the enhanced Nappi-Witten algebra. The advantages of considering the Lie algebra expansion procedure is also discussed.

On the structure of polynomial roots

2021 ◽  
Vol 105 (563) ◽  
pp. 253-262
Author(s):  
R. W. D. Nickalls
Keyword(s):  
Underlying Structure ◽  
Polynomial Roots ◽  
Polynomial Degree

This Article explores how root multiplicity and polynomial degree influence the structure of the roots of a univariant polynomial. After setting up the notation, we draw upon a result derived in [1], and show that all polynomial roots have a common underlying structure comprising just five parameters. Finally we present some examples involving the lower polynomials.

scholarly journals A new family of weighted one-parameter flux reconstruction schemes

2021 ◽  
Vol 222 ◽  
pp. 104918
Author(s):  
W. Trojak ◽  
F.D. Witherden
Keyword(s):  
Flux Reconstruction ◽  
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