Discontinuous Galerkin Methods

A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: closed (15 November 2022) | Viewed by 2051

Special Issue Editor


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Guest Editor
Department of Mathematics, Chinese University of Hong Kong, Hong Kong, China
Interests: discontinuous Galerkin methods; computational wave propagation; fluid flow in heterogeneous media; multiscale model reduction techniques; adaptivity for multiscale problems; domain decomposition methods; data-driven computational methods; numerical upscaling
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Special Issue Information

Dear Colleagues,

Discontinuous Galerkin methods are widely employed in computational science and engineering fields, as they offer accurate and efficient simulations. The development, analysis and applications of discontinuous Galerkin methods have thus stimulated significant research. This Special Issue aims to create a platform for papers for the exchange of knowledge on all aspects of discontinuous Galerkin methods.

This Special Issue will present the latest scientific advances, reviews, communications, and short notes considering discontinuous Galerkin methods.

Prof. Dr. Eric Chung
Guest Editor

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Published Papers (1 paper)

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Research

21 pages, 4106 KiB  
Article
An Adaptive in Space, Stabilized Finite Element Method via Residual Minimization for Linear and Nonlinear Unsteady Advection–Diffusion–Reaction Equations
by Juan F. Giraldo and Victor M. Calo
Math. Comput. Appl. 2023, 28(1), 7; https://doi.org/10.3390/mca28010007 - 06 Jan 2023
Cited by 3 | Viewed by 1279
Abstract
We construct a stabilized finite element method for linear and nonlinear unsteady advection–diffusion–reaction equations using the method of lines. We propose a residual minimization strategy that uses an ad-hoc modified discrete system that couples a time-marching schema and a semi-discrete discontinuous Galerkin formulation [...] Read more.
We construct a stabilized finite element method for linear and nonlinear unsteady advection–diffusion–reaction equations using the method of lines. We propose a residual minimization strategy that uses an ad-hoc modified discrete system that couples a time-marching schema and a semi-discrete discontinuous Galerkin formulation in space. This combination delivers a stable continuous solution and an on-the-fly error estimate that robustly guides adaptivity at every discrete time. We show the performance of advection-dominated problems to demonstrate stability in the solution and efficiency in the adaptivity strategy. We also present the method’s robustness in the nonlinear Bratu equation in two dimensions. Full article
(This article belongs to the Special Issue Discontinuous Galerkin Methods)
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