Work

On the Compact Discontinuous Galerkin Method for Polytopal Meshes

Year: 2026

Type: article

Abstract: . The compact discontinuous Galerkin method was introduced by Peraire and Persson in (SIAM J. Sci. Comput., 30, 1806–1824, 2008). In this work, we present the stability and convergence analysis for the [Formula: see text]-version of this method applied to elliptic problems on polytopal meshes. Moreover, we introduce fast and practical algorithms that allow the CDG, LDG, and BR2 methods to be implemented within a unified framework. Our numerical experiments show that the CDG method yields a compact stencil for the stiffness matrix, with faster assembly and solving times compared to the LDG and BR2 methods. We numerically study how coercivity depends on the method parameters for various mesh types, with particular focus on the number of facets per mesh element. Finally, we demonstrate the importance of choosing the correct directions for the numerical fluxes when using variable polynomial degrees.

Source: SIAM Journal on Scientific Computing

DOI: 10.1137/26m184057x

Authors: Mattia Corti, Sergio Gómez

Institutions: University of Vienna, Politecnico di Milano, Istituto di Matematica Applicata e Tecnologie Informatiche, University of Milano-Bicocca

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Austrian Science Fund, Gruppo Nazionale per il Calcolo Scientifico

Awards: G3878859087, G5377794632