Using a decomposition of the global error into a locally created part and a propagating component, we derive residual-based two-sided local a posteriori error bounds for the locally created component of the global error for Petrov-Galerkin approximations of symmetric positive systems in the sense of Friedrichs. The performance of the a local error indicators is illustrated by a series of numeri...

Variational formulations of time-dependent PDEs in space and time yield (d + 1)-dimensional problems to be solved numerically. This increases the number unknowns as well storage amount. On other hand, this approach enables adaptivity model reduction w.r.t. both type variables. In paper, we show that matrix oriented techniques can significantly reduce computational timings for solving arising li...