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This paper describes a direct solver algorithm for a sequence of finiteelement meshes that are h-refined towards one or several point singularities.For such a sequence of grids, the solver delivers linear computational costO(N) in terms of CPU time and memory with respect to the number of unknowns N.The linear computational cost is achieved by utilizing the recursive structureprovided by the sequence of h-adaptive grids with a special construction of theelimination tree that allows for reutilization of previously computed partialLU factorizations over the entire unrefined part of the computational mesh. Thereutilization technique reduces the computational cost of the entire sequenceof h-refined grids from O(N^2) down to O(N). Theoretical estimates areillustrated with numerical results on two- and three-dimensional model problemsexhibiting one or several point singularities.

A direct solver with reutilization of previously-computed LU factorizations for h-adaptive finite element grids with point singularities