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\title{An  ALE Method Incorporating Conserved Monitor Functions}

\author{Mike Baines 
University of Reading, UK}

\date{ }

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\maketitle
One way of constructing a moving mesh for an ALE simulation 
is to introduce a monitor function which drives the Jacobian
 of the ALE mapping.  The method is
consistent with the Geometric Conservation Law.
 The monitor function can be chosen to locally 
enforce invariance properties such as conservation,
 as in Geometric
Integration. 

The potential of the approach is illustrated in a
 scalar context for 
nonlinear diffusion and advection equations. Finite
 Volume and Finite Element approaches are described.
 Monitor functions based solely 
on invariance or on shape preservation are only
 partially successful but there 
is also the possiblility of constructing combination
 monitors which depend on bot

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