davidm/notes-fd-staircase.txt

## notes-fd-staircase.txt
One method I've prototyped to reduce effects of finite difference (F.D.) staircase effects (though not really recommended nor used but provided for reference):

(1) Solve the partial differential equation for f in the usual way by F.D.
(2) Measure f and grad(f) at each point about one or two mesh units away from the boundary surface by using data from #1.  Use this to update values at boundary condition mesh points.  For example, by linear extrpolation or other extrapolation technique.
(3) Repeat #1 until convergence.

Other obvious variations for updating boundary mesh point values are possible, including expressing #1-3 as a single matrix equation to solve (which probably has some equivalence to currently used techniques), thereby avoiding the repetition needed in #3.
	One method I've prototyped to reduce effects of finite difference (F.D.) staircase effects (though not really recommended nor used but provided for reference):

	(1) Solve the partial differential equation for f in the usual way by F.D.
	(2) Measure f and grad(f) at each point about one or two mesh units away from the boundary surface by using data from #1. Use this to update values at boundary condition mesh points. For example, by linear extrpolation or other extrapolation technique.
	(3) Repeat #1 until convergence.

	Other obvious variations for updating boundary mesh point values are possible, including expressing #1-3 as a single matrix equation to solve (which probably has some equivalence to currently used techniques), thereby avoiding the repetition needed in #3.