## Asymptotic Error Analysis of Finite Difference Methods

- Date: 03/11/2008

Brian Wetton, UBC

University of British Columbia

When computing approximations to PDE problems with

smooth solutions using regular grids, the error has additional

structure. For second order methods applied to elliptic or parabolic

problems, an expansion for the error can be constructed that is regular

in the grid spacing. This expansion can be used to justify convergence

for nonlinear problems, and is an easy way to see why convergence with

higher regularity is observed (a phenomena sometimes called

superconvergence in the FE community). When artificial boundary

conditions are introduced for higher order finite difference methods,

numerical boundary layers result. Identifying the types of errors that

are generated by a given scheme and the order at which they occur can

be called Asymptotic Error Analysis. Several examples of the technique

and its uses will be given. This will be an overview talk also with

some material useful to anyone trying to implement "unusual" boundary

conditions for PDE problems.

**UBC SCAIM Seminar**