Among a variety of grid deformation methods, the method proposed by Liao
[4, 6, 18] is one of the most favourables, because it prevents mesh tangling and offers
precise control over the element volumes. Its numerical realisation only requires
solving a Poisson problem and a system of fully decoupled initial value problems.
Many other deformation methods in contrast involve the solution of complex nonlinear
PDEs. In this article, we introduce a generalisation of Liao’s method which
allows for generating a desired mesh size distribution for quite arbitrary grids without
giving rise to mesh tangling. We elaborate on its numerical realisation and prove
the convergence of our method. Our results are confirmed by numerical experiments.