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We study computational complexity aspects for Finite Element formulationsconsidering hypercubic space--time full and time--marching discretizationschemes for $h$--refined grids towards singularities. We perform a relativelycomprehensive study of comparing the computational time via time complexitiesof direct and iterative solvers. We focus on the space-time formulation withrefined computational grids and on the corresponding time slabs, namely,computational grids obtained by taking the "cross-sections" of the refinedspace-time mesh. We compare the computational complexity of the space-timeformulation and the corresponding time--marching scheme. Our considerationconcerns the computational complexity of the multi-frontal solvers, theiterative solvers, as well as the static condensation. Numerical experimentswith Octave confirm our theoretical findings.

Complexity of direct and iterative solvers on space-time formulations versus time--marching schemes for h-refined grids towards singularities