Robust Globally Divergence-Free Weak Galerkin Finite Element Methods for Unsteady Natural Convection Problems
Year: 2019
Author: Hongliang Li, Xiaoping Xie, Yihui Han, Hongliang Li, Xiaoping Xie
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 4 : pp. 1266–1308
Abstract
This paper proposes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady natural convection problems in two and three dimensions. In the space discretization, the methods use piecewise polynomials of degrees $k,$ $k-1,$ and $k$ $(k\geq 1)$ for the velocity, pressure and temperature approximations in the interior of elements, respectively, and piecewise polynomials of degree $k$ for the numerical traces of velocity, pressure and temperature on the interfaces of elements. In the temporal discretization of the fully discrete method, the backward Euler difference scheme is adopted. The semi-discrete and fully discrete methods yield globally divergence-free velocity solutions. Well-posedness of the semi-discrete scheme is established and a priori error estimates are derived for both the semi-discrete and fully discrete schemes. Numerical experiments demonstrate the robustness and efficiency of the methods.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2019-0069
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 4 : pp. 1266–1308
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 43
Keywords: Unsteady natural-convection semi-discrete and fully discrete weak Galerkin method globally divergence-free error estimate.
Author Details
-
A weak Galerkin method for the nonlinear Navier–Stokes problem
Zhao, Jingjun
Lv, Zhiqiang
Xu, Yang
Computational and Applied Mathematics, Vol. 43 (2024), Iss. 1
https://doi.org/10.1007/s40314-023-02580-8 [Citations: 0]