Enforcement of essential boundary conditions in meshless approximations using finite elements

A technique for easily treating essential boundary conditions for approximations which are not interpolants, such as moving least-square approximations in the element-free Galerkin method, is presented. The technique employs a string of elements along the essential boundaries and combines the finite element shape functions with the approximation. In the resulting approximation, essential boundary conditions can be treated exactly as in finite elements. It is shown that the resulting approximation can exactly reproduce linear polynomials so that it satisfies the patch test. Numerical studies show that the method retains the high rate of convergence associated with moving least-square approximations.