scholarly journals L2stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods

2008 ◽  
Vol 42 (4) ◽  
pp. 593-607 ◽  
Author(s):  
Yingjie Liu ◽  
Chi-Wang Shu ◽  
Eitan Tadmor ◽  
Mengping Zhang
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Discontinuous Galerkin Methods ◽  
Galerkin Methods ◽  
Central Discontinuous Galerkin

scholarly journals Capitalizing on Superconvergence for More Accurate Multi-Resolution Discontinuous Galerkin Methods

2021 ◽  
Author(s):  
Jennifer K. Ryan
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Discontinuous Galerkin Methods ◽  
Galerkin Methods ◽  
Accurate Approximation ◽  
Siac Filtering ◽  
Multi Resolution Analysis ◽  
Resolution Analysis

AbstractThis article focuses on exploiting superconvergence to obtain more accurate multi-resolution analysis. Specifically, we concentrate on enhancing the quality of passing of information between scales by implementing the Smoothness-Increasing Accuracy-Conserving (SIAC) filtering combined with multi-wavelets. This allows for a more accurate approximation when passing information between meshes of different resolutions. Although this article presents the details of the SIAC filter using the standard discontinuous Galerkin method, these techniques are easily extendable to other types of data.

scholarly journals A Modified Discontinuous Galerkin Method for Solving Efficiently Helmholtz Problems

2012 ◽  
Vol 11 (2) ◽  
pp. 335-350 ◽  
Author(s):  
Magdalena Grigoroscuta-Strugaru ◽  
Mohamed Amara ◽  
Henri Calandra ◽  
Rabia Djellouli
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Discontinuous Galerkin Methods ◽  
Galerkin Methods ◽  
Two Dimensional ◽  
Local Problems ◽  
The Stability ◽  
Well Posed ◽  
Solution Methodology

AbstractA new solution methodology is proposed for solving efficiently Helmholtz problems. The proposed method falls in the category of the discontinuous Galerkin methods. However, unlike the existing solution methodologies, this method requires solving (a) well-posed local problems to determine the primal variable, and (b) a global positive semi-definite Hermitian system to evaluate the Lagrange multiplier needed to restore the continuity across the element edges. Illustrative numerical results obtained for two-dimensional interior Helmholtz problems are presented to assess the accuracy and the stability of the proposed solution methodology.

A Weakly Penalized Discontinuous Galerkin Method for Radiation in Dense, Scattering Media

2016 ◽  
Vol 16 (4) ◽  
pp. 563-577
Author(s):  
Guido Kanschat ◽  
José Pablo Lucero Lorca
Keyword(s):  
Asymptotic Analysis ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Discontinuous Galerkin Methods ◽  
Radiation Transport ◽  
Isotropic Scattering ◽  
Galerkin Methods ◽  
Penalty Parameter ◽  
Scattering Media

AbstractWe review the derivation of weakly penalized discontinuous Galerkin methods for scattering dominated radiation transport and extend the asymptotic analysis to non-isotropic scattering. We focus on the influence of the penalty parameter on the edges and derive a new penalty for interior edges and boundary fluxes. We study how the choice of the penalty parameters influences discretization accuracy and solver speed.

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