A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
An Interior a Priori Estimate for Parabolic Difference Operators and an Application

1971
*
Mathematics of Computation
*

A general class of finite-difference approximations to a parabolic system of differential equations in a bounded domain fi is considered. It is shown that if a solution Uh of the discrete problem converges in a discrete L1 norm to a solution U of the continuous problem as the mesh size A tends to zero, then the difference quotients of Uh converge to the corresponding derivatives of U, the convergence being uniform on any compact subset of Q. In particular, Uh converges uniformly on compact

doi:10.2307/2005131
fatcat:ujns4abq7vcuzffojfam36vp2m