Fourier analysis for discontinuous Galerkin and related methods

• 来源期刊: 科学通报（英文版）
• 年，卷（期）: 2009,（11）
• 页码范围: 1809-1816
• 页数: 8页
• 语种: 英文
• DOI: 10.1007/s11434-009-0365-2

摘要

In this paper we review a series of recent work on using a Fourier analysis technique to study the sta-bility and error estimates for the discontinuous Galerkin method and other related schemes. The ad-vantage of this approach is that it can reveal instability of certain "bad"' schemes; it can verify stability for certain good schemes which are not easily amendable to standard finite element stability analysis techniques; it can provide quantitative error comparisons among different schemes; and it can be used to study superconvergence and time evolution of errors for the discontinuous Galerkin method. We will briefly describe this Fourier analysis technique, summarize its usage in stability and error estimates for various schemes, and indicate the advantages and disadvantages of this technique in comparison with other finite element techniques.