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Research Article | Open Access

Efficiency analysis of continuous and discontinuous Galerkin finite element methods

Hanifa Hanif1,2( ), Jan Nordström3,4( ), Arnaud. G. Malan1
InCFD Research Group, Department of Mechanical Engineering, University of Cape Town, Cape Town 7700, South Africa
Department of Mathematics, Sardar Bahadur Khan Women's University, Quetta, Pakistan
Department of Mathematics, Linköping University, SE–581 83 Linköping, Sweden
Department of Mathematics, University of Johannesburg, Auckland Park 2006, Johannesburg, South Africa
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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.

Keywords

stability, convergenceefficiencysummation by partscontinuous Galerkin methoddiscontinuous Galerkin method
CLC number: 65M12, 65M22, 65M60

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AIMS Mathematics
Volume 10 Issue 9,
September 2025
Pages 22579-22597
DOI: 10.3934/math.20251005

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Cite this article:
Hanif H, Nordström J, Malan AG. Efficiency analysis of continuous and discontinuous Galerkin finite element methods. AIMS Mathematics, 2025, 10(9): 22579-22597. https://doi.org/10.3934/math.20251005

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Received: 09 July 2025
Revised: 14 September 2025
Accepted: 24 September 2025
Published: 29 September 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)