Time-accurate solution of stabilized convection-diffusion-reaction equations: I. Time and space discretization

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

Volume: 18, Issue 8
Pages: 565 – 573
Date: 2002


The paper addresses the development of time accurate methods for solving transient
convection- diffusion-reaction problems using fifinite elements. Multi-stage time
stepping schemes of high accuracy are used. They are first combined with a Galerkin
formulation to briefly recall the time space discretization. Then spatial stabilization
techniques are combined with high-order time stepping schemes. Moreover, a least-squares
formulation is also developed for these high-order time schemes combined with
Cº finite elements (in spite of the diffusion operator and without reducing
the strong form into a system of first-order differential equations). The weak
forms induced by the SUPG, GLS, SGS and least-squares formulations are presented
and compared. In a companion paper (Part II of this work), the phase and damping
properties of the developed schemes are analyzed and numerical examples are included
to confirm the effectiveness of the proposed methodology for solving time dependent
convection-diffusion-reaction problems.



  Author   = {Antonio Huerta and Jean Donea},
  Title    = {Time-accurate solution of stabilized convection-diffusion-reaction equations: {I} --- {T}ime and space discretization},
  Fjournal = {Communications in Numerical Methods in Engineering},
  Journal  = {Commun. Numer. Methods Eng.},
  Volume   = {18},
  Number   = {8},
  Pages    = {565--573},
  Year     = {2002}}