The intrinsic partition of unity method

A method is presented which enables the global enrichment of the approximation space without introducing additional unknowns. Only one shape function per node is used. The shape functions are constructed by means of the moving least-squares method with an intrinsic basis vector and weight functions based on finite element shape functions. The enrichment is achieved through the intrinsic basis. By using polynomials in the intrinsic basis, optimal rates of convergence can be achieved even on distorted elements. Special enrichment functions can be chosen to enhance accuracy for solutions that are not polynomial in character. Results are presented which show optimal convergence on randomly distorted elements and improved accuracy for the oscillatory solution of the Helmholtz equation.