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See Chapters 1 and 2 of Huang and Russell: Adaptive Moving Mesh Methods (Springer, New York, 2011) for the detailed description of the methods and examples.

All programs in a gzipped file: all.tar.gz
Gradient recovery: grad_recovery.m
Compute the interpolation error:
interpolation_error.m
Smooth the density function (rho):
mesh_density_fnct_smoothing.m
Compute the density function (rho):
mesh_density_fnct.m
Mesh generation using De Boor's algorithm:
meshgen_deboor.m
Mesh generation using MMPDE5:
meshgen_mmpde5.m
Mesh generation using MMPDE5 (explicit integration) :
meshgen_mmpde5ex.m
Mesh generation using MMPDE5xi:
meshgen_mmpde5xi.m
Mesh generation using the twopoint BVP algorithm:
meshgen_tpbvp.m
Moving mesh finite difference method: movfdm.m
Moving mesh finite element method: movfem.m
Finite difference PDE solver on a fixed mesh: pdefdm.m
Compute mesh quality measures: qmesh.m
Example driver for Section 1.2 (FDM):
sec1_2_burgersFDM.m
Example driver for Section 1.3 (FEM):
sec1_3_burgersFEM.m
Example driver for Section 1.4 (moving mesh FDM):
sec1_4_burgersFDM.m
Example driver for Section 1.4 (fixed mesh FDM):
sec1_4_burgersFDMFixedMesh.m
Example driver for Examples 1 and 2 of Section 2.2:
sec2_2ex1ex2.m
Example driver for Examples 1 and 2 of Section 2.3:
sec2_3ex1ex2.m
Example driver for Example 1 of Section 2.5:
sec2_5ex1.m
Example driver for Example 2 of Section 2.5:
sec2_5ex2.m
Example driver for Example 3 of Section 2.5:
sec2_5ex3.m