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- W2890749070 abstract "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 <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mn>4</m:mn> <m:mo>/</m:mo> <m:mn>3</m:mn> </m:mrow> </m:math> {4/3} -CFL condition ( <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mi mathvariant=normal>Δ</m:mi> <m:mo></m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo>∼</m:mo> <m:msup> <m:mi>h</m:mi> <m:mrow> <m:mn>4</m:mn> <m:mo>/</m:mo> <m:mn>3</m:mn> </m:mrow> </m:msup> </m:mrow> </m:math> {Delta tsim 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 <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mi>L</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> {L^{2}} -sense and obtain quasi-optimal convergence for smooth solution in space and time for piecewise polynomials with any degree <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>l</m:mi> <m:mo>≥</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> {lgeq 1} under the standard CFL condition." @default.
- W2890749070 created "2018-09-27" @default.
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- W2890749070 date "2018-09-11" @default.
- W2890749070 modified "2023-09-25" @default.
- W2890749070 title "A Priori Error Analysis of a Discontinuous Galerkin Scheme for the Magnetic Induction Equation" @default.
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- W2890749070 doi "https://doi.org/10.1515/cmam-2018-0032" @default.
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