Efficiency analysis of continuous and discontinuous Galerkin finite element methods

Hanifa Hanif; Jan Nordström; Arnaud G. Malan

doi:10.3934/math.20251005

Efficiency analysis of continuous and discontinuous Galerkin finite element methods

Hanifa Hanif
, Jan Nordström
, Arnaud G. Malan

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We present a comparative analysis of the continuous Galerkin (CG) and discontinuous Galerkin (DG) finite element (FE) methods, focusing on their efficiency in solving advection–diffusion problems in the Summation By Parts–Simultaneous Approximation Term (SBP–SAT) framework. Our findings provide insights into the practical advantages and limitations of each approach, guiding future applications in high–order numerical simulations of real world applications.

Original language	English
Pages (from-to)	22579-22597
Number of pages	19
Journal	AIMS Mathematics
Volume	10
Issue number	9
DOIs	https://doi.org/10.3934/math.20251005
Publication status	Published - 2025

Keywords

continuous Galerkin method
discontinuous Galerkin method
efficiency
stability, convergence
summation by parts

ASJC Scopus subject areas

General Mathematics

Access to Document

10.3934/math.20251005

Cite this

@article{d23c6bf8318e4a59be30d56dc3660910,

title = "Efficiency analysis of continuous and discontinuous Galerkin finite element methods",

abstract = "We present a comparative analysis of the continuous Galerkin (CG) and discontinuous Galerkin (DG) finite element (FE) methods, focusing on their efficiency in solving advection–diffusion problems in the Summation By Parts–Simultaneous Approximation Term (SBP–SAT) framework. Our findings provide insights into the practical advantages and limitations of each approach, guiding future applications in high–order numerical simulations of real world applications.",

keywords = "continuous Galerkin method, discontinuous Galerkin method, efficiency, stability, convergence, summation by parts",

author = "Hanifa Hanif and Jan Nordstr{\"o}m and Malan, \{Arnaud G.\}",

note = "Publisher Copyright: {\textcopyright} 2025 the Author(s).",

year = "2025",

doi = "10.3934/math.20251005",

language = "English",

volume = "10",

pages = "22579--22597",

journal = "AIMS Mathematics",

issn = "2473-6988",

publisher = "American Institute of Mathematical Sciences",

number = "9",

}

TY - JOUR

T1 - Efficiency analysis of continuous and discontinuous Galerkin finite element methods

AU - Hanif, Hanifa

AU - Nordström, Jan

AU - Malan, Arnaud G.

PY - 2025

Y1 - 2025

N2 - We present a comparative analysis of the continuous Galerkin (CG) and discontinuous Galerkin (DG) finite element (FE) methods, focusing on their efficiency in solving advection–diffusion problems in the Summation By Parts–Simultaneous Approximation Term (SBP–SAT) framework. Our findings provide insights into the practical advantages and limitations of each approach, guiding future applications in high–order numerical simulations of real world applications.

AB - We present a comparative analysis of the continuous Galerkin (CG) and discontinuous Galerkin (DG) finite element (FE) methods, focusing on their efficiency in solving advection–diffusion problems in the Summation By Parts–Simultaneous Approximation Term (SBP–SAT) framework. Our findings provide insights into the practical advantages and limitations of each approach, guiding future applications in high–order numerical simulations of real world applications.

KW - continuous Galerkin method

KW - discontinuous Galerkin method

KW - efficiency

KW - stability, convergence

KW - summation by parts

UR - https://www.scopus.com/pages/publications/105017899015

U2 - 10.3934/math.20251005

DO - 10.3934/math.20251005

M3 - Article

AN - SCOPUS:105017899015

SN - 2473-6988

VL - 10

SP - 22579

EP - 22597

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 9

ER -

Efficiency analysis of continuous and discontinuous Galerkin finite element methods

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this