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The lowest-degree stabilizer-free weak Galerkin finite element method for Poisson equation on rectangular and triangular meshes | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 9، دوره 13، شماره 2، مهر 2022، صفحه 83-94 اصل مقاله (889.23 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.24411.2736 | ||
| نویسندگان | ||
| Allahbakhsh Yazdani Cherati* 1؛ Hamid Momeni2 | ||
| 1Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran | ||
| 2Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar Iran | ||
| تاریخ دریافت: 10 شهریور 1400، تاریخ بازنگری: 05 آبان 1400، تاریخ پذیرش: 09 آبان 1400 | ||
| چکیده | ||
| Recently, the study on weak Galerkin (WG) methods with or without stabilizer parameters has received much attention. The WG methods are a discontinuous extension of the standard finite element methods in which classical differential operators are approximated on functions with discontinuity. A stabilizer term in the WG formulation is used to guarantee convergence and stability of the discontinuous approximations for a model problem. By removing this parameter, we can reduce the complexity of programming on this numerical method. Our goal in this paper is to introduce a new stabilizer-free WG (SFWG) method to solve the Poisson equation in which we use a new combination of WG elements. Numerical experiments indicate that our SFWG scheme is faster and more economical than the standard WG scheme. Errors and convergence rates on two types of mesh are presented for each of the considered methods, which show that our numerical scheme has $O(h^2)$ convergence rate while another method has $O(h)$ convergence rate in the energy norm and the $L^2$-norm. | ||
| کلیدواژهها | ||
| Stabilizer-free weak Galerkin؛ Discrete weak differential operators؛ The Poisson equation؛ Rectangular mesh؛ Lowest-degree elements | ||
| مراجع | ||
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