  The development of higher order finite elements methods has become an active
research area. The deformation method for mesh generation has achieved a
prescribed positive Jacobian determinant constraint and it has been a useful
method for mesh adaptation. In this work, the deformation method is combined
with local refinement to generate higher order meshes. 2D and 3D numerical
examples of element order p=3 are shown to demonstrate the effectiveness of our
new algorithm.
