Weighted finite element method and body of optimal parameters for elasticity problem with singularity

Abstract

Mathematical models with a singularity play a decisive role in predicting the development of processes in fracture mechanics. A weighted finite element method based on the introduction of the definition of an Rν-generalized solution for the system of Lamé equations with corner singularity is constructed. An estimate for the convergence of an approximate solution by a weighted finite element method to an Rν-generalized solution at a rate of O(h), that is, without loss of accuracy, is proved. For effective use of a weighted finite element method, it is necessary to correctly set the control parameters of the approach for performing calculations. An algorithm for determining the optimal parameters the weighted finite element method for finding an approximate solution to the Lamé system in domains with a boundary containing re-entrant corners ranging from π to 2π is developed. The general body of optimal parameters for weighted finite element method is determined.