An r-adaptive finite element method based upon moving mesh PDEs

We present an r-adaptive finite element method for solving time dependent partial differential equations. A moving mesh partial differential equation, or MMPDE, is used to move the (unstructured) mesh in time. A key to the application of the MMPDE to unstructured mesh movement is to define a computational domain and then compute the corresponding computational mesh as the image of an initial mesh on the given physical domain. The finite element discretization of physical PDEs on moving meshes is addressed. Numerical results are presented to demonstrate the capability of the mesh movement strategy and the r-adaptive finite element method. A fully developed r-adaptive finite element method can be expected to be ideally suited to complement the currently popular h-p finite element methods and to provide increased reliability and efficiency for mesh adaptation. (C) 1999 Academic Press.