Yazdani Cherati, Allahbakhsh, Momeni, Hamid. (1401). The lowest-degree stabilizer-free weak Galerkin finite element method for Poisson equation on rectangular and triangular meshes. هنرهای کاربردی, 13(2), 83-94. doi: 10.22075/ijnaa.2021.24411.2736
Allahbakhsh Yazdani Cherati; Hamid Momeni. "The lowest-degree stabilizer-free weak Galerkin finite element method for Poisson equation on rectangular and triangular meshes". هنرهای کاربردی, 13, 2, 1401, 83-94. doi: 10.22075/ijnaa.2021.24411.2736
Yazdani Cherati, Allahbakhsh, Momeni, Hamid. (1401). 'The lowest-degree stabilizer-free weak Galerkin finite element method for Poisson equation on rectangular and triangular meshes', هنرهای کاربردی, 13(2), pp. 83-94. doi: 10.22075/ijnaa.2021.24411.2736
Yazdani Cherati, Allahbakhsh, Momeni, Hamid. The lowest-degree stabilizer-free weak Galerkin finite element method for Poisson equation on rectangular and triangular meshes. هنرهای کاربردی, 1401; 13(2): 83-94. doi: 10.22075/ijnaa.2021.24411.2736

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
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
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