Resumen de A new Pretov-Galerkin scheme for the two-point boundary value problem

Rodolfo Araya , Gabriel N. Gatica

• This paper introduces a new asymptotically convergent Petrov-Galerkin method for solving the two-point boundary value problem. The procedure is based on an appropriate combination of a Dirichlet-Neumann mapping and a saddle point variational formulation of the original problem, which yields a bilinear form satisfying the usual Gårding inequality. The corresponding discrete scheme is defined in the usual manner but replacing the Dirichlet-Neumann mapping by its associated finite element approximation. The solvability of the Galerkin equations is proved,and asymptotic error estimates are provided. Further, a particular case of this new scheme can be viewed as a preconditioning technique for the discrete formulation of the saddle point problem. Finally, the matrix formulation is discussed and several numerical experiments are included.