Convergence Analysis of an Unconditionally Energy Stable Projection Scheme for Magneto-Hydrodynamic Equations

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 (δt ≤ 1/√log(h)| for 2D and δt ≤ √h for 3D), the optimal error estimate for the pressure is derived as well.

Department(s)

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

MHD; Stability; Finite element method; Error estimate; Projection

International Standard Serial Number (ISSN)

0168-9274; 1873-5460

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 Elsevier, All rights reserved.

Publication Date

01 Feb 2019

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