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Algorithms for multi-adaptive time-stepping

Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations. In particular, the multi-adaptive methods allow individual time steps to be used for different components or in different regions of space. We present algorithms for multi-adaptive time-stepping, including the recursive construction of time slabs, regulation of the individual time steps, adaptive fixed point iteration on time slabs, and the automatic generation of dual problems. An example is given for the solution of a nonlinear partial differential equation in three dimensions.