FEM is a valuable approximation tool for the solution of Partial Differential Equations when the analytical solutions are difficult or impossible to obtain due to complicated geometry or boundary conditions. The Project work involved collecting facts related to WG and DG‑FEMs. WG‑FEM is a numerical method that was first proposed and analyzed by Wang and Ye (2013) for general second‑order elliptic BVPs on triangular and rectangular meshes. DG‑FEMs as developed by Cockburn et al. (1970) uses a discontinuous function space to approximate the exact solution of the equations. The comparison and numerical examples demonstrated that WG‑FEMs are viable and hold some advantages over DG‑FEMs, due to their properties. Numerical examples demonstrated that WGM generates a smaller linear system to solve than the DGMs. WG‑FEM have less unknowns, no need for choosing penalty factor and normal flux is continuous across element interfaces compared to DG‑FEMs and the implementation of WG‑FEMs is easier than that of DG‑FEMs based on error and convergence rate. The computations were done by hand and with the help of MATLAB 2021Rb.
| Published in | International Journal of Systems Science and Applied Mathematics (Volume 7, Issue 2) |
| DOI | 10.11648/j.ijssam.20220702.11 |
| Page(s) | 23-38 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Finite Element Method (FEM), Galerkin Method, Weak Galerkin FEM, Discontinuous Galerkin FEM
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APA Style
Desta Sodano Sheiso. (2022). Comparative Study of Weak Galerkin and Discontinuous Galerkin Finite Element Methods. International Journal of Systems Science and Applied Mathematics, 7(2), 23-38. https://doi.org/10.11648/j.ijssam.20220702.11
ACS Style
Desta Sodano Sheiso. Comparative Study of Weak Galerkin and Discontinuous Galerkin Finite Element Methods. Int. J. Syst. Sci. Appl. Math. 2022, 7(2), 23-38. doi: 10.11648/j.ijssam.20220702.11
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Download@article{10.11648/j.ijssam.20220702.11,
author = {Desta Sodano Sheiso},
title = {Comparative Study of Weak Galerkin and Discontinuous Galerkin Finite Element Methods},
journal = {International Journal of Systems Science and Applied Mathematics},
volume = {7},
number = {2},
pages = {23-38},
doi = {10.11648/j.ijssam.20220702.11},
url = {https://doi.org/10.11648/j.ijssam.20220702.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20220702.11},
abstract = {FEM is a valuable approximation tool for the solution of Partial Differential Equations when the analytical solutions are difficult or impossible to obtain due to complicated geometry or boundary conditions. The Project work involved collecting facts related to WG and DG‑FEMs. WG‑FEM is a numerical method that was first proposed and analyzed by Wang and Ye (2013) for general second‑order elliptic BVPs on triangular and rectangular meshes. DG‑FEMs as developed by Cockburn et al. (1970) uses a discontinuous function space to approximate the exact solution of the equations. The comparison and numerical examples demonstrated that WG‑FEMs are viable and hold some advantages over DG‑FEMs, due to their properties. Numerical examples demonstrated that WGM generates a smaller linear system to solve than the DGMs. WG‑FEM have less unknowns, no need for choosing penalty factor and normal flux is continuous across element interfaces compared to DG‑FEMs and the implementation of WG‑FEMs is easier than that of DG‑FEMs based on error and convergence rate. The computations were done by hand and with the help of MATLAB 2021Rb.},
year = {2022}
}
TY - JOUR T1 - Comparative Study of Weak Galerkin and Discontinuous Galerkin Finite Element Methods AU - Desta Sodano Sheiso Y1 - 2022/05/31 PY - 2022 N1 - https://doi.org/10.11648/j.ijssam.20220702.11 DO - 10.11648/j.ijssam.20220702.11 T2 - International Journal of Systems Science and Applied Mathematics JF - International Journal of Systems Science and Applied Mathematics JO - International Journal of Systems Science and Applied Mathematics SP - 23 EP - 38 PB - Science Publishing Group SN - 2575-5803 UR - https://doi.org/10.11648/j.ijssam.20220702.11 AB - FEM is a valuable approximation tool for the solution of Partial Differential Equations when the analytical solutions are difficult or impossible to obtain due to complicated geometry or boundary conditions. The Project work involved collecting facts related to WG and DG‑FEMs. WG‑FEM is a numerical method that was first proposed and analyzed by Wang and Ye (2013) for general second‑order elliptic BVPs on triangular and rectangular meshes. DG‑FEMs as developed by Cockburn et al. (1970) uses a discontinuous function space to approximate the exact solution of the equations. The comparison and numerical examples demonstrated that WG‑FEMs are viable and hold some advantages over DG‑FEMs, due to their properties. Numerical examples demonstrated that WGM generates a smaller linear system to solve than the DGMs. WG‑FEM have less unknowns, no need for choosing penalty factor and normal flux is continuous across element interfaces compared to DG‑FEMs and the implementation of WG‑FEMs is easier than that of DG‑FEMs based on error and convergence rate. The computations were done by hand and with the help of MATLAB 2021Rb. VL - 7 IS - 2 ER -
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