Optimal upstream collocation: A survey of recent results

Stephen H. Brill

doi:10.1016/S0167-5648(04)80079-0

Optimal upstream collocation: A survey of recent results

Stephen H. Brill

Mathematics Department

Research output: Contribution to journal › Article › peer-review

Abstract

We give herein analytical formulas for the Hermite collocation solution of the steady-state convection-diffusion equation with Dirichlet boundary conditions defined on a uniform mesh in one spatial dimension. Analysis is provided that compares the discrete collocation solution to the corresponding exact solution. Extremely accurate collocation solutions are easily attainable in a variety of settings by utilizing the author's "optimal upstream weighting" technique.

Original language	English
Pages (from-to)	531-542
Number of pages	12
Journal	Developments in Water Science
Volume	55
Issue number	PART 1
DOIs	https://doi.org/10.1016/S0167-5648(04)80079-0
State	Published - 2004

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abstract = "We give herein analytical formulas for the Hermite collocation solution of the steady-state convection-diffusion equation with Dirichlet boundary conditions defined on a uniform mesh in one spatial dimension. Analysis is provided that compares the discrete collocation solution to the corresponding exact solution. Extremely accurate collocation solutions are easily attainable in a variety of settings by utilizing the author's {"}optimal upstream weighting{"} technique.",

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AB - We give herein analytical formulas for the Hermite collocation solution of the steady-state convection-diffusion equation with Dirichlet boundary conditions defined on a uniform mesh in one spatial dimension. Analysis is provided that compares the discrete collocation solution to the corresponding exact solution. Extremely accurate collocation solutions are easily attainable in a variety of settings by utilizing the author's "optimal upstream weighting" technique.

UR - https://www.scopus.com/pages/publications/80051595011

U2 - 10.1016/S0167-5648(04)80079-0

DO - 10.1016/S0167-5648(04)80079-0

M3 - Article

AN - SCOPUS:80051595011

SN - 0167-5648

VL - 55

SP - 531

EP - 542

JO - Developments in Water Science

JF - Developments in Water Science

IS - PART 1

ER -

Optimal upstream collocation: A survey of recent results

Abstract

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