The method of constructing of Dirichlet boundary value problem basis for variational methods

Abstract

The method of basis constructing for the approximation of functions which are satisfying the homogeneous Dirichlet condition on two-dimensional domain boundary based on cubic B-splines is presented in the paper. The new basis consists of B-splines, if their supports lie in the closure of the domain under consideration, and boundary basic elements which account for boundary conditions and interface with the standard basis inside the domain. It is shown that boundary basic elements do not degrade the approximation properties of cubic splines.