The Orthonormalized Generalized Finite Element MethodOGFEM: Efficient and stable reduction of approximation errors through multiple orthonormalized enriched basis functions
The shortcomings of generalized/extended finite element methods are illustrated. A procedure to construct orthonormal enriched basis functions is proposed (OGFEM). The condition number of the unconstrained system matrix is equal to one in the OGFEM. We elaborate on the applicability of the OGFEM in finite precision arithmetic. The OGFEM improves the rate at which the approximation solution converges to the exact solution substantially for the 1D modified Helmholtz and Poisson equations.
orthonormality condition number gfem xfem sgfem improved convergence