[cig-commits] commit: Added paragraph about stability

[Mercurial]

changeset:   154:a42afc877c82
tag:         tip
user:        Matthew G Knepley <knepley at gmail.com>
date:        Tue Dec 18 08:02:44 2012 -0500
files:       faultRup.tex
description:
Added paragraph about stability


diff -r 6088bf21a991 -r a42afc877c82 faultRup.tex
--- a/faultRup.tex	Thu Sep 13 14:12:40 2012 -0700
+++ b/faultRup.tex	Tue Dec 18 08:02:44 2012 -0500
@@ -711,6 +711,14 @@ slip-weakening \citep{Ida:1972}, linear 
 \citep{Andrews:2004}, and Dieterich-Ruina rate-state friction with an
 aging law \citep{Dieterich:1979}. See the PyLith manual
 \citep{PyLith:manual:1.7.1} for details.
+
+Notice that the matrix $\bm{L}$ defined in equation~(\ref{eqn:jacobian:constraint})
+is spectrally equivalent to the identity, since it just involves a rotation
+into the local fault coordinate system. This makes the traditional LBB stability
+criterion trivial to satisfy by choosing the space of Lagrange multipliers to be
+exactly the space of displacements, restricted to the fault. In simple terms, in
+order to specify the problem we need to know the distance between any pair of
+fault vertices $(v^+,v^-)$, which can be expressed as a displacement.
 
 % ------------------------------------------------------------------
 \section{Finite-Element Mesh Processing}