Robust Globally Divergence-Free Weak Galerkin Finite Element Methods for Natural Convection Problems
Year: 2019
Author: Yihui Han, Xiaoping Xie
Communications in Computational Physics, Vol. 26 (2019), Iss. 4 : pp. 1039–1070
Abstract
This paper proposes and analyzes a class of weak Galerkin (WG) finite element methods for stationary natural convection problems in two and three dimensions. We use piecewise polynomials of degrees k, k−1, and k (k ≥1) for the velocity, pressure, and temperature approximations in the interior of elements, respectively, and piecewise polynomials of degrees l, k, l (l=k−1, k) for the numerical traces of velocity, pressure and temperature on the interfaces of elements. The methods yield globally divergence-free velocity solutions. Well-posedness of the discrete scheme is established, optimal a priori error estimates are derived, and an unconditionally convergent iteration algorithm is presented. Numerical experiments confirm the theoretical results and show the robustness of the methods with respect to Rayleigh number.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0107
Communications in Computational Physics, Vol. 26 (2019), Iss. 4 : pp. 1039–1070
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Natural convection weak Galerkin method globally divergence-free error estimate Rayleigh number.