Time-accurate solution of stabilized convection-diffusion-reaction equations: II. Accuracy analysis and examples

Author (s): Antonio Huerta, Bernardino Roig and Jean Donea
Journal: Communications in Numerical Methods in Engineering

Volume: 18, Issue 8
Pages: 575 – 584
Date: 2002

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 analyzed 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
(SUPG, GLS, SGS and least-squares) do not degrade the phase accuracy. Finally, some examples are presented to show the applicability of these schemes.



  Author   = {Antonio Huerta and Bernardino Roig and Jean Donea},
  Title    = {Time-accurate solution of stabilized convection-diffusion-reaction equations: {II} --- {A}ccuracy analysis and examples},
  Fjournal = {Communications in Numerical Methods in Engineering},
  Journal  = {Commun. Numer. Methods Eng.},
  Volume   = {18},
  Number   = {8},
  Pages    = {575--584},
  Year     = {2002}}