应用DG方法的新型局部变差间断监测器（英文）

New DiscontinuityIndicator for DG Method UsingLocal Variation

受到总变差有界(TVB)方法中总变差概念的启示,提出适用于间断伽辽金(DG)方法的局部变差概念.在此基础上,对Soblev空间中的误差估计进行严格的界定,建立一种能够准确甄别激波与接触间断等间断位置的新型识别器.研究结果表明:与有限体积方法中的间断监测器相比,该新型识别器完全基于单元局部,不需要依靠相邻单元的任何信息,具有典型的有限元方法的固有属性,更容易在算法上实现.通过典型的数值算例对该识别器进行验证,结果表明:该识别器非常出色地实现对间断位置的识别,可用于间断元方法的间断位置监测.

Inspired by the concept of total variation in the total variation bounded（TVB）methods,a similar concept of local variation for discontinuous Galerkin（DG）method was presented.Based on the local variation,a rigorous bounding procedure for error evaluation in the Soblev′s space was conducted,and then a new type of discontinuity indicator was developed to detect the locations of discontinuities such as shock and contact et al.Compared with the detectors in the finite volume method,the new indicator is completely local within an element and does not rely on any information from neighboring elements.As a result,the indicator features intrinsic characteristics of the finite element method and is very simple to implement.The typical numerical examples show a good performance of the newly constructed indicator and it becomes a proper candidate for detecting tasks of DG applications.