  We describe a framework for controlling and improving the quality of
high-order finite element meshes based on extensions of the Target-Matrix
Optimization Paradigm (TMOP) of Knupp. This approach allows high-order
applications to have a very precise control over local mesh quality, while
still improving the mesh globally. We address the adaption of various TMOP
components to the settings of general isoparametric element mappings, including
the mesh quality metric in 2D and 3D, the selection of sample points and the
solution of the resulting mesh optimization problem. We also investigate
additional practical concerns, such as tangential relaxation and restricting
the deviation from the original mesh. The benefits of the new high-order TMOP
algorithms are illustrated on a number of test problems and examples from a
high-order arbitrary Eulerian-Lagrangian (ALE) application. Our implementation
is freely available in an open-source library form.
