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

University of Cape Town
Sardar Bahadur Khan Women’s University
Linköping University

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

1 Citation (Scopus)

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

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10.3934/math.20251005

Cite this

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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.",

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AU - Nordström, Jan

AU - Malan, Arnaud G.

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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

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DO - 10.3934/math.20251005

M3 - Article

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ER -

Efficiency analysis of continuous and discontinuous Galerkin finite element methods

Abstract

Keywords

ASJC Scopus subject areas

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