A local space-time adaptive scheme in solving two-dimensional parabolic problems based on domain decomposition methods

We describe a local space-time adaptive refinement and derefinement method for solving systems of parabolic partial differential equations. Solutions are calculated on local spacetime meshes using a domain decomposition finit e element algorithm in space and an extrapolation algorithm in time. An a p osteriori spatial error estimate controls a local spatial refinement strate gy and an a posteriori temporal error estimate monitors temporal refinement and order of the integration. A multiplicative Schwarz algorithm is used t o coordinate solutions between overlapping grids. We use nearly minimal ne meshes which follow the dynamics of the problems in an efficient manner.