Continuously deforming finite elements for convection dominated flows

A continuously deforming finite element method is developed from a new variational formulation which employs a general time-dependent coordinate transformation. Both the solution field and coordinate transformation enter as unknowns in the resulting variational statement. Hence the mesh evolves with the solution and the method is particularly well suited to convection-dominated transport processes. Constraints governing permissible distortion of the elements are enforced using local penalties. Representative one- and two-dimensional example problems have been computed and sample results are included here.