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# Computational Methods in Applied Mathematics

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# A Priori Error Analysis of a Discontinuous Galerkin Scheme for the Magnetic Induction Equation

Tanmay Sarkar
• Corresponding author
• Tata Instiute of Fundamental Research, Centre for Applicable Mathematics, Post Bag No. 6503, GKVK Post Office, Sharada Nagar, Chikkabommasandra, Bangalore 560065; and Department of Mathematics, Indian Institute of Technology Jammu, NH-44 Bypass Road, Jagti, Jammu 181 221, India
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Published Online: 2018-09-11 | DOI: https://doi.org/10.1515/cmam-2018-0032

## Abstract

We perform the error analysis of a stabilized discontinuous Galerkin scheme for the initial boundary value problem associated with the magnetic induction equations using standard discontinuous Lagrange basis functions. In order to obtain the quasi-optimal convergence incorporating second-order Runge–Kutta schemes for time discretization, we need a strengthened $4/3$-CFL condition ($\mathrm{\Delta }t\sim {h}^{4/3}$). To overcome this unusual restriction on the CFL condition, we consider the explicit third-order Runge–Kutta scheme for time discretization. We demonstrate the error estimates in ${L}^{2}$-sense and obtain quasi-optimal convergence for smooth solution in space and time for piecewise polynomials with any degree $l\ge 1$ under the standard CFL condition.

MSC 2010: 65M60; 65M12; 65M15; 76W05

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Revised: 2018-07-20

Accepted: 2018-08-08

Published Online: 2018-09-11

Citation Information: Computational Methods in Applied Mathematics, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840,

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