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Abstract In this paper, we study a finite element approximation for a linear, first-order in time, unconditionally energy stable scheme proposed in [7] for solving the magneto-hydrodynamic equations. We first… Click to show full abstract
Abstract In this paper, we study a finite element approximation for a linear, first-order in time, unconditionally energy stable scheme proposed in [7] 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 ( δ t ≤ 1 / | l o g ( h ) | for 2D and δ t ≤ h for 3D), the optimal error estimate for the pressure is derived as well.
Journal Title: Applied Numerical Mathematics
Year Published: 2019
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