  A new functional is presented for variational mesh generation and adaptation.
It is formulated based on combining the equidistribution and alignment
conditions into a single condition with only one dimensionless parameter. The
functional is shown to be coercive but not convex. A solution procedure using a
discrete moving mesh partial differential equation is employed. It is shown
that the element volumes and altitudes of a mesh trajectory of the mesh
equation associated with the new functional are bounded away from zero and the
mesh trajectory stays nonsingular if it is so initially. Numerical examples
demonstrate that the new functional performs comparably as an existing one that
is also based on the equidistribution and alignment conditions and known to
work well but contains an additional parameter.
