The Optimal L2-Norm Error Estimate of a Weak Galerkin Finite Element Method for a Multi-Dimensional Evolution Equation with a Weakly Singular Kernel
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| Publicado en: | Fractal and Fractional vol. 9, no. 6 (2025), p. 368-382 |
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MDPI AG
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| Acceso en línea: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| 001 | 3223905874 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2504-3110 | ||
| 024 | 7 | |a 10.3390/fractalfract9060368 |2 doi | |
| 035 | |a 3223905874 | ||
| 045 | 2 | |b d20250101 |b d20251231 | |
| 100 | 1 | |a Zhou Haopan |u Bangor College, Central South University of Forestry and Technology, Changsha 410004, China; 20227879@csuft.edu.cn | |
| 245 | 1 | |a The Optimal <i>L</i><sup>2</sup>-Norm Error Estimate of a Weak Galerkin Finite Element Method for a Multi-Dimensional Evolution Equation with a Weakly Singular Kernel | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a This paper proposes a weak Galerkin (WG) finite element method for solving a multi-dimensional evolution equation with a weakly singular kernel. The temporal discretization employs the backward Euler scheme, while the fractional integral term is approximated via a piecewise constant function method. A fully discrete scheme is constructed by integrating the WG finite element approach for spatial discretization. <inline-formula>L2</inline-formula>-norm stability and convergence analysis of the fully discrete scheme are rigorously established. Numerical experiments are conducted to validate the theoretical findings and demonstrate optimal convergence order in both spatial and temporal directions. The numerical results confirm that the proposed method achieves an accuracy of the order <inline-formula>Oτ+hk+1</inline-formula>, where <inline-formula>τ</inline-formula> and h represent the time step and spatial mesh size, respectively. This work extends previous studies on one-dimensional problems to higher spatial dimensions, providing a robust framework for handling evolution equations with a weakly singular kernel. | |
| 653 | |a Finite element method | ||
| 653 | |a Finite volume method | ||
| 653 | |a Approximation | ||
| 653 | |a Evolution | ||
| 653 | |a Finite element analysis | ||
| 653 | |a Fractional calculus | ||
| 653 | |a Convergence | ||
| 653 | |a Charged particles | ||
| 653 | |a Galerkin method | ||
| 653 | |a Estimates | ||
| 653 | |a Discretization | ||
| 700 | 1 | |a Zhou, Jun |u College of Computer Science and Mathematics, Central South University of Forestry and Technology, Changsha 410004, China; hongbinchen@csuft.edu.cn | |
| 700 | 1 | |a Chen, Hongbin |u College of Computer Science and Mathematics, Central South University of Forestry and Technology, Changsha 410004, China; hongbinchen@csuft.edu.cn | |
| 773 | 0 | |t Fractal and Fractional |g vol. 9, no. 6 (2025), p. 368-382 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3223905874/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3223905874/fulltextwithgraphics/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3223905874/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |