We study computational complexity aspects for Finite Element formulations considering hypercubic space--time full and time--marching discretization schemes for h--refined grids towards singularities. We perform a relatively comprehensive study of comparing the computational time via time complexities of direct and iterative solvers. We focus on the space-time formulation with refined computational grids and on the corresponding time slabs, namely, computational grids obtained by taking the "cross-sections" of the refined space-time mesh. We compare the computational complexity of the space-time formulation and the corresponding time--marching scheme. Our consideration concerns the computational complexity of the multi-frontal solvers, the iterative solvers, as well as the static condensation. Numerical experiments with Octave confirm our theoretical findings.
@article{arxiv.2110.05804,
title = {Complexity of direct and iterative solvers on space-time formulations versus time--marching schemes for h-refined grids towards singularities},
author = {Marcin Skotniczny and Anna Paszynska and Sergio Rojas and Maciej Paszynski},
journal= {arXiv preprint arXiv:2110.05804},
year = {2022}
}