A Review of Continuous and Discontinuous Galerkin Finite Element Methodfor Differential Equations

Authors

  • 1,2Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq.
  • 1,2Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq.

Abstract

This study is a review of both the continuous Galerkin finite element method (CGFEM)and the
discontinuous Galerkin finite element method (DGFEM).A group of the most important research over the
last 13 years has been compared to both methods and their historical development, as well as comparing
the advantages and disadvantages of both methods.This review is aimed at determining the best and most
efficient method to solve complex problems in the future.

References

AbdulRidha, M. W., &Kashkool, H. A. (2019). The Error Analysis for the Discontinuous Galerkin

Finite Element Method of the Convection-Diffusion Problem. Journal of Basrah Researches

((Sciences)), 45(2).

AbdulRidha, M. W., &Kashkool, H. A. (2022, August). Space-time Petrov-discontinuous Galerkin

finite element method for solving linear convection-diffusion problems. In Journal of Physics:

Conference Series (Vol. 2322, No. 1, p. 012007). IOP Publishing.

Al-Jaberi, A. K., & Hameed, E. M. (2021, May). Topological Data Analysis For Evaluating PDEbased

Denoising Models. In Journal of Physics: Conference Series (Vol. 1897, No. 1, p. 012006).

IOP Publishing.

Al-Jaberi, A. K., Asaad, A., Jassim, S. A., & Al-Jawad, N. (2018, May). Topological data analysis to

improve exemplar-based inpainting. In Mobile Multimedia/Image Processing, Security, and

Applications 2018 (Vol. 10668, p. 1066805). International Society for Optics and Photonics.

Al-Jaberi, A. K., Asaad, A., Jassim, S. A., & Al-Jawad, N. (2020). Topological Data Analysis for

Image Forgery Detection. Indian Journal of Forensic Medicine & Toxicology, 14(3), 1745.

Al-Jaberi, A. K., Jassim, S. A., & Al-Jawad, N. (2018, May). Colorizing monochrome images.

In Mobile Multimedia/Image Processing, Security, and Applications 2018 (Vol. 10668, p.

. International Society for Optics and Photonics.

An, N., Huang, C., & Yu, X. (2019). Error analysis of direct discontinuous Galerkin method for the

two-dimensional fractional diffusion-wave equation. Applied Mathematics and Computation, 349,

-157.

Anca, A., Cardona, A., Risso, J., &Fachinotti, V. D. (2011). Finite element modeling of welding

processes. Applied Mathematical Modelling, 35(2), 688-707.

Argyris, J. H., & Kelsey, S. (1960). Energy theorems and structural analysis (Vol. 60). London:

Butterworths.

Arnold, D. N., Brezzi, F., Cockburn, B., & Marini, L. D. (2002). Unified analysis of discontinuousGalerkin methods for elliptic problems. SIAM journal on numerical analysis, 39(5), 1749-1779.

Baker, G. A. (1977). Finite element methods for elliptic equations using nonconforming elements.

Mathematics of Computation, 31(137), 45-59.

Cangiani, A., Georgoulis, E. H., &Sabawi, Y. A. (2020). Convergence of an adaptive discontinuous

Galerkin method for elliptic interface problems. Journal of Computational and Applied

Mathematics, 367, 112397.

Cesmelioglu, A., Cockburn, B., &Qiu, W. (2017). Analysis of a hybridizable discontinuous

Galerkinmethod for the steady-state incompressible Navier-Stokes equations. Mathematics of

Computation, 86(306), 1643-1670.

Chen, H., Fan, D., Huang, J., Huang, W., Zhang, G., & Huang, L. (2020). Finite element analysis

model on ultrasonic phased array technique for material defect time of flight diffraction detection.

Science of Advanced Materials, 12(5), 665-675.

Clough, R. W. (1960). The finite element method in plane stress analysis. In Proceedings of2nd

ASCE Conference on Electronic Computation, Pittsburgh Pa., Sept. 8 and 9, 1960.

Cockburn, B., Karniadakis, G. E., & Shu, C. W. (Eds.). (2012). Discontinuous Galerkin methods:

theory, computation, and applications (Vol. 11). Springer Science & Business Media.

Cohen, G., &Pernet, S. (2017). Finite element and discontinuous Galerkin methods for transient

wave equations. Dordrecht: Springer.

Dziuk, G., & Elliott, C. M. (2013). Finite element methods for surface PDEs. Acta Numerica, 22,

-396.

Feireisl, E., &Luk

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Published

2023-07-13