Abstract
Based on an extension of the discontinuous Galerkin finite element method, discretization schemes for solving parabolic problems on grids with local refinement, both in space and in time, are constructed. The stability of schemes constructed in this way is automatically ensured by the method. The construction of two-level preconditioners utilizing local timestepping and a global coarse-grid solver both on standard, rectangular, and uniform grids, is the main objective of the paper. The optimal convergence properties of such two-level preconditioners are studied. The theory is illustrated by a set of numerical examples.
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