  This paper describes a direct solver algorithm for a sequence of finite
element meshes that are h-refined towards one or several point singularities.
For such a sequence of grids, the solver delivers linear computational cost
O(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 structure
provided by the sequence of h-adaptive grids with a special construction of the
elimination tree that allows for reutilization of previously computed partial
LU factorizations over the entire unrefined part of the computational mesh. The
reutilization technique reduces the computational cost of the entire sequence
of h-refined grids from O(N^2) down to O(N). Theoretical estimates are
illustrated with numerical results on two- and three-dimensional model problems
exhibiting one or several point singularities.
