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 finite element algorithm in space and an extrapolation algorithm in time. An a posteriori spatial error estimate controls a local spatial refinement strategy and an a posteriori temporal error estimate monitors temporal refinement and order of the integration. A multiplicative Schwarz algorithm is used to coordinate solutions between overlapping grids. We use nearly minimal ne meshes which follow the dynamics of the problems in an efficient manner. [References: 23]
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