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A PU localization for space-time goal oriented adaptive refinement of non-stationary PDEs
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In this talk, we will present our space-time extension of the spatial variational partition or unity (PU) approach for localization of dual weighted residual (DWR) type error estimators. This allows for estimation and control of both spatial and temporal errors w.r.t. a given quantity of interest. Additionally, we will discuss the tensor-product framework for discretizing space-time PDEs, which uses the space- time weak formulation directly. This allows for a flexible choice of the temporal polynomial FE order without the need of deriving classical time-stepping schemes. Finally, numerical results with applications to complex fluids substantiate our developments.
