Practical Aspects of Formulation and Solution of Moving Mesh Partial Differential Equations

Moving mesh partial differential equations (MMPDEs) are used in the MMPDE moving mesh method to generate adaptive moving meshes for the numerical solution of time dependent problems. How MMPDEs are formulated and solved is crucial to the efficiency and robustness of the method. In this paper, several practical aspects of formulating and solving MMPDEs are studied. They include spatial balance, scaling invariance, effective control of mesh concentration, bounds on time steps, multiple sub-steps, and two-level mesh movement. Numerical results are also given.