A New Functional for Variational Mesh Generation and Adaptation Based on Equidistribution and Alignment Conditions

摘要

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