Time-accurate solution of stabilized convection-diffusion-reaction equations: II - accuracy analysis and examples
The paper addresses the development of time-accurate methods for solving transient convection-diffusion -reaction problems using finite elements. The accuracy characteristics of the spatially stabilized implicit multi-stage time-stepping schemes developed in a companion paper (Part I of this work) are analysed and compared here. This is done by means of a Fourier analysis. An important improvement is observed when the order of the method is increased. Moreover, the stabilization techniques proposed (streamline-upwind Petrov-Galerkin (SUPG), Galerkin least-square (GLS), sub-grid scale (SGS) and least squares) do not degrade the phase accuracy. Finally, some examples are presented to show the applicability of these schemes.
CitationHuerta, A.; Roig, B.; Donea, J. Time-accurate solution of stabilized convection-diffusion-reaction equations: II - accuracy analysis and examples. "Communications in numerical methods in engineering", Agost 2002, vol. 18, núm. 8, The definitive version is available at http://www3.interscience.wiley.com/journal/93520035/abstract, p. 575-584.