Convergence of discontinuous Galerkin schemes for the Euler equations via dissipative weak solutions
作者：
Highlights：
• Introduction of dissipative weak solutions for the Euler equations in the framework of high-order FE methods.
• First investigation of convergence of high-order FE schemes in terms of dissipative weak solutions for the Euler equations.
• Consistency analysis of high-order DG methods without any underlying smoothness assumptions.
• Recipe of obtaining a convergence result in terms of dissipative weak solutions.
• Numerical validation of convergence using Cesaro averages for the Kelvin–Helmholtz problem.
摘要
•Introduction of dissipative weak solutions for the Euler equations in the framework of high-order FE methods.•First investigation of convergence of high-order FE schemes in terms of dissipative weak solutions for the Euler equations.•Consistency analysis of high-order DG methods without any underlying smoothness assumptions.•Recipe of obtaining a convergence result in terms of dissipative weak solutions.•Numerical validation of convergence using Cesaro averages for the Kelvin–Helmholtz problem.
论文关键词：Euler equations,Dissipative weak solutions,Convergence analysis,Discontinuous Galerkin,Structure preserving
论文评审过程：Received 16 March 2022, Revised 20 July 2022, Accepted 23 August 2022, Available online 5 September 2022, Version of Record 5 September 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127508
