ABSTRACT
The purpose of this chapter is to discuss the introduction of mesh movement for steady PDEs in multidimensions, using mesh locations as additional parameters. In this way we may seek an optimal mesh at the same time as finding a converged solution on that mesh. When the mesh locations are included in the parameters of the space discretization, an extended system of ordinary differential equations (ODEs) or differential algebraic equations (DAEs) is normally obtained which includes both mesh and solution parameters in a coupled way. Integration of these equations may then be carried out using the MOL, although there is a wide variety of approaches.
