High resolution, minimal storage algorithms for convection dominated, convection-diffusion equations. (English) Zbl 0625.76095

Ervin, V.; Layton, W.

Applied mathematics and computing, Trans. 4th Army Conf., Ithaca/N.Y. 1986, ARO Rep. 87-1, 1173-1201 (1987).

[For the entire collection see Zbl 0614.00003.]
Several new methods for the numerical solution of convection dominated, convection-diffusion equations are presented. These methods are high accuracy methods and, in some cases, monotone schemes. Further, they can be implemented in a way as to require only an asymptotically negligible increase in storage over usual first order methods. Thus they are promising candidates for vectorization. Numerical experiments are presented and some error estimates, proven by the authors for these schemes, are reviewed.

MSC:

76R50	Diffusion
35Q30	Navier-Stokes equations
35K57	Reaction-diffusion equations
76M99	Basic methods in fluid mechanics

Keywords:

numerical solution; convection dominated, convection-diffusion equations; high accuracy methods; monotone schemes; first order methods; vectorization; error estimates