论文信息 - Necessary L2-uniform convergence conditions for difference schemes for two-dimensional convection-diffusion problems

Necessary L2-uniform convergence conditions for difference schemes for two-dimensional convection-diffusion problems

We derive necessary conditions for the uniform convergence (with respect to the perturbation parameter) in L2 of schemes for singularly perturbed convection-diffusion problems. Applying these conditions, we show that the convergence order of the streamline diffusion finite element method with piecewise linear trial functions cannot be better than 12, uniformly in the singular perturbation parameter.

Lutz Tobiska | Martin Stynes | M. Stynes | L. Tobiska

[1] Wil H. A. Schilders,et al. Uniform Numerical Methods for Problems with Initial and Boundary Layers , 1980 .

[2] T. Hughes,et al. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[3] M. Stynes,et al. A globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions , 1991 .

[4] I. Babuska,et al. On locking and robustness in the finite element method , 1992 .

[5] Martin Stynes,et al. A Comparison of Uniformly Convergent Difference Schemes for Two-Dimensional Convection-Diffusion Problems , 1993 .

[6] Gerard R. Richter,et al. The discontinuous Galerkin method with diffusion , 1992 .

[7] H. G. Roos. Necessary convergence conditions for upwind schemes in the two‐dimensional case , 1985 .

[8] Herbert Goering,et al. Singularly perturbed differential equations , 1983 .

[9] Koichi Niijima,et al. Pointwise error estimates for a streamline diffusion finite element scheme , 1989 .