High-order accurate time-stepping schemes for convection-diffusion problems

Author (s): Donéa, J., Roig, B. and Huerta, A.
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 182, Issues 3, 4
Pages: 249 – 275
Date: 2000

The paper discusses the formulation of high-order accurate time-stepping schemes for transient convection-diffusion problems to be combined with finite element methods of the least-squares type for a stable discretization of highly convective problems. Padé approximations of the exponential function are considered for deriving multi-stage time integration schemes involving first time derivatives only, thus easier to implement in conjunction with Cº finite elements than standard time-stepping schemes which incorporate higher order time derivatives. After a brief discussion of the stability and accuracy properties of the multi-stage Padé schemes and having underlined the similarity between Padé and Runge-Kutta methods, the paper closes with the presentation of illustrative examples which indicate the effectiveness of the proposed methods.



  Author   = {Jean Donea and Bernardino Roig and Antonio Huerta},
  Title    = {High-order accurate time-stepping schemes for convection-diffusion problems},
  Fjournal = {Computer Methods in Applied Mechanics and Engineering},
  Journal  = {Comput. Methods Appl. Mech. Eng.},
  Volume   = {182},
  Number   = {3--4},
  Pages    = {249--275},
  Year     = {2000}}