High-order accurate time-stepping schemes for convection-diffusion problems
The paper discusses the formulation of high-order accurate time-stepping schemes for transient convectiondiffusion problems to be combined with finite element methods of the least-squares type for a stable discretization of highly convective problems. Pad 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 C0 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 Pad schemes and having underlined the similarity between Pad and RungeKutta methods, the paper closes with the presentation of illustrative examples which indicate the effectiveness of the proposed methods.
time-stepping schemes convectiondiffusion finite elements pad approximants