Convergence Analysis of an Unconditionally Energy Stable Projection Scheme for Magneto-Hydrodynamic Equations
In this paper, we study a finite element approximation for a linear, first-order in time, unconditionally energy stable scheme proposed in  for solving the magneto-hydrodynamic equations. We first reformulate the semi-discrete scheme to the fully discrete version and then carry out a rigorous stability and error analysis for it. We show that the fully discrete scheme indeed leads to optimal error estimates for both velocity and magnetic field with some reasonable regularity assumptions. Moreover, under an alleviated time step constraint (δt ≤ 1/√log(h)| for 2D and δt ≤ √h for 3D), the optimal error estimate for the pressure is derived as well.
X. Yang et al., "Convergence Analysis of an Unconditionally Energy Stable Projection Scheme for Magneto-Hydrodynamic Equations," Applied Numerical Mathematics, vol. 136, pp. 235-256, Elsevier, Feb 2019.
The definitive version is available at https://doi.org/10.1016/j.apnum.2018.10.013
Mathematics and Statistics
Keywords and Phrases
MHD; Stability; Finite element method; Error estimate; Projection
International Standard Serial Number (ISSN)
Article - Journal
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