Application of an adaptive finite element method to solve evolution heat transfer problems

Abstract

The adapcive refinemenr/derefinemenc processes of nested grids are very useful to solve time-dependent problems in which moving refinement areas are required. In this paper our derefinement algorithm is briefly explained. The efficiency of the algorithm is showed in a nurnerical example: a time-dependent convection-diffusion problem. The derefinement algorithm enables us to use the multigrid method in order to solve the equation system associated to the finite-element method. The additional computation time required by this algorithm amounts less than 1 % of total execution time. The derefinement algorithm can be also used for local refining. Dereffining after global refinement is thereby equivalent to a local refinement procedure, not requiring the use of error indicators. The algorithm promises to be very useful in more complex problems including non linearity where we need to adapt the mesh to a changing solution.