# Cost of space-time formulations: a study on the performance of direct and iterative solvers on space-time formulations versus time-marching schemes

@article{Skotniczny2021CostOS, title={Cost of space-time formulations: a study on the performance of direct and iterative solvers on space-time formulations versus time-marching schemes}, author={Marcin Skotniczny and Anna Paszynska and Maciej Paszyński}, journal={ArXiv}, year={2021}, volume={abs/2110.05804} }

We focus on finite element method computations for time-dependent problems. We prove that the computational cost of the space-time formulation is higher than the cost of the time-marching schemes. This applies to both direct and iterative solvers. It concerns both uniform and adaptive grids. The only exception from this rule is the h adaptive space-time simulation of the traveling point object, resulting in refinements towards their trajectory in the space-time domain. However, if this object…

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