The comparative analysis of adaptive algorithms in the finite element method for solving boundary value problem for the stationary reaction-diffusion equation
The new adaptive algorithm of construction of a grid in the $hp$-version of a finite element method with piecewise-polynomial basis functions, oriented on solving a boundary value problem having local singularity for the one-dimensional reaction-diffusion equations is offered. The algorithm ensures smoothing of a grid solution by adaptive elimination and adding of nodes of a grid. Comparison with the algorithm offered earlier in which for an adaptive mesh refinement and removal of nodes are based on the estimation of local effect from trial adding new and removals of old basis functions is spent. Results of numerical experiments for an estimation of efficiency of the offered algorithm on the singular perturbed modelling problem with a smooth solution are presented.