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.

Other Information: