A discrete commutator theory for the consistency and phase error analysis of semi-discrete C-0 finite element approximations to the linear transport equation

作者：Thompson Travis^*

来源：Journal of Computational and Applied Mathematics, 2016, 303: 229-248.

DOI：10.1016/j.cam.2016.02.042

• Finite elements
• Transport equation
• Consistency error
• Mass lumping
• Dispersion error
• Superconvergence

A novel method, based on a discrete commutator, for the analysis of consistency error and phase relations for semi-discrete continuous finite element approximation of the one-way wave equation is presented. The technique generalizes to arbitrary dimension, accommodates the use of compatible quadratures, does not require the use of complex calculations, is applicable on non-uniform mesh geometries, and is especially useful when conventional Taylor series or Fourier approaches are intractable. Following the theory the analysis method is demonstrated for several test cases.

• 出版日期2016-9