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<p>We prove <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10915_2025_3036_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-stability of an explicit second order Runge-Kutta discontinuous Galerkin (RKDG2) method for two classes of nonlinear convex scalar conservation laws in one space dimension under the Courant-Friedrichs-Lewy (CFL) condition <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10915_2025_3036_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta t \sim \Delta x\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>∼</mo> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </math></EquationSource> </InlineEquation>. We only consider uniform mesh and periodic boundary conditions.</p>

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\(L^2\)-Stability Of Explicit Second Order Runge-Kutta Discontinuous Galerkin Method For Nonlinear Conservation Laws

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Yuanzhe Wei,
  • Chi-Wang Shu

摘要

We prove \(L^2\) L 2 -stability of an explicit second order Runge-Kutta discontinuous Galerkin (RKDG2) method for two classes of nonlinear convex scalar conservation laws in one space dimension under the Courant-Friedrichs-Lewy (CFL) condition \(\Delta t \sim \Delta x\) Δ t ∼ Δ x . We only consider uniform mesh and periodic boundary conditions.