Abstract:
The paper analyzes the $h$-$p$ version of the finite element method for a one-dimensional model boundary
value problem with coordinated degeneration of initial data and with strong singularity of a solution. The
scheme of the finite element method is constructed on the basis of the definition of $R_\nu$-generalized solution to the problem, and the finite element space contains singular power functions. By using meshes with concentration at a singular point and by constructing the linear degree vector of approximating functions in
a special way, a nearly optimal two-sided exponential estimate is obtained for the residual of the finite element method.
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