A Unified Error Analysis of Hybridizable Discontinuous Galerkin Methods for the Static Maxwell Equations

2020 ◽  
Vol 58 (2) ◽  
pp. 1367-1391 ◽  
Author(s):  
Shukai Du ◽  
Francisco-Javier Sayas
Keyword(s):  
Error Analysis ◽  
Discontinuous Galerkin ◽  
Maxwell Equations ◽  
Discontinuous Galerkin Methods ◽  
Galerkin Methods ◽  
Hybridizable Discontinuous Galerkin ◽  
Hybridizable Discontinuous Galerkin Methods

scholarly journals Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Minam Moon ◽  
Hyung Kyu Jun ◽  
Tay Suh
Keyword(s):  
Approximate Solution ◽  
Discontinuous Galerkin ◽  
Computer Simulations ◽  
Parabolic Equations ◽  
Discontinuous Galerkin Methods ◽  
Numerical Technique ◽  
Galerkin Methods ◽  
Hybridizable Discontinuous Galerkin ◽  
Hybridizable Discontinuous Galerkin Methods ◽  
Error Estimations

HDG method has been widely used as an effective numerical technique to obtain physically relevant solutions for PDE. In a practical setting, PDE comes with nonlinear coefficients. Hence, it is inevitable to consider how to obtain an approximate solution for PDE with nonlinear coefficients. Research on using HDG method for PDE with nonlinear coefficients has been conducted along with results obtained from computer simulations. However, error analysis on HDG method for such settings has been limited. In this research, we give error estimations of the hybridizable discontinuous Galerkin (HDG) method for parabolic equations with nonlinear coefficients. We first review the classical HDG method and define notions that will be used throughout the paper. Then, we will give bounds for our estimates when nonlinear coefficients obey “Lipschitz” condition. We will then prove our main result that the errors for our estimations are bounded.

scholarly journals The pursuit of a dream, Francisco Javier Sayas and the HDG methods

SeMA Journal ◽  
2021 ◽  
Author(s):  
Bernardo Cockburn
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
University Of Delaware ◽  
Galerkin Methods ◽  
Hybridizable Discontinuous Galerkin ◽  
Static Condensation ◽  
The Usa ◽  
Hybridizable Discontinuous Galerkin Methods ◽  
Background Material ◽  
The University

AbstractFranciso Javier Sayas, man of grit and determination, left his hometown of Zaragoza in 2007 in pursuit of a dream, to become a scholar in the USA. I hosted him in Minneapolis, where he spent three long years of an arduous transition before obtaining a permanent position at the University of Delaware. There, he enthusiastically worked on the unfolding of his dream until his life was tragically cut short by cancer, at only 50. In this paper, I try to bring to light the part of his academic life he shared with me. As we both worked on hybridizable discontinuous Galerkin methods, and he wrote a book on the subject, I will tell Javier’s life as it developed around this topic. First, I will show how the ideas of static condensation and hybridization, proposed back in the mid 60s, lead to the introduction of those methods. This background material will allow me to tell the story of the evolution of the hybridizable discontinuous Galerkin methods and describe Javier’s participation in it. Javier faced death with open eyes and poised dignity. I will end with a poem he liked.

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