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Matlab Programs for 1D Adaptive Moving Mesh Methods

This page contains the matlab programs for moving mesh finite difference and finite element methods for the numerical solution of systems of 1D second-order parabolic equations. They can also be used for fixed meshes. Programs for adaptive mesh generation and several example drivers are also provided.

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 two-point 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