NOTICE: Due to a lapse in annual appropriations, most of this website is not being updated. Learn more.
Form submissions will still be accepted but will not receive responses at this time. Sections of this site for programs using non-appropriated funds (such as NVLAP) or those that are excepted from the shutdown (such as CHIPS and NVD) will continue to be updated.
An official website of the United States government
Here’s how you know
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
Data assimilation in 2D nonlinear advection diffusion equations, using an explicit stabilized leapfrog scheme run backward in time.
Published
Author(s)
Alfred S. Carasso
Abstract
With an artificial example of a 2D nonlinear advection diffusion equation on the unit square this paper considers the data assimilation problem of finding initial values that can evolve into a close approximation to a desired target result at some realistic T > 0. Highly non smooth target data are considered, that may not correspond to actual solutions at time T, and it may not be possible to find such initial values. The aim is to illustrate the inherent difficulties of the ill-posed data assimilation problem. 1,1 Top
Carasso, A.
(2022),
Data assimilation in 2D nonlinear advection diffusion equations, using an explicit stabilized leapfrog scheme run backward in time., Technical Note (NIST TN), National Institute of Standards and Technology, Gaithersburg, MD, [online], https://doi.org/10.6028/NIST.TN.2227, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=934984
(Accessed October 2, 2025)