In this paper, we develop and analyze a finite element projection method for magnetohydrodynamics equations in Lipschitz domain. A fully discrete scheme based on Euler semi-implicit method is proposed, in which continuous elements are used to approximate the Navier–Stokes equations and H(curl) conforming Nédélec edge elements are used to approximate the magnetic equation. One key point of the projection method is to be compatible with two different spaces for calculating velocity, which leads one to obtain the pressure by solving a Poisson equation. The results show that the proposed projection scheme meets a discrete energy stability. In addition, with the help of a proper regularity hypothesis for the exact solution, this paper provides a rigorous optimal error analysis of velocity, pressure and magnetic induction. Finally, several numerical examples are performed to demonstrate both accuracy and efficiency of our proposed scheme.
Q. Ding et al., "Error Analysis of a Fully Discrete Projection Method for Magnetohydrodynamic System," Numerical Methods for Partial Differential Equations, vol. 39, no. 2, pp. 1449 - 1477, Wiley, Mar 2023.
The definitive version is available at https://doi.org/10.1002/num.22941
Mathematics and Statistics
Keywords and Phrases
Error Analysis; Finite Element Method; Magnetohydrodynamics; Nédélec Edge Element; Projection Methods
International Standard Serial Number (ISSN)
Article - Journal
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01 Mar 2023