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

• Araya, Rodolfo A. ^[1] ; Gatica, Gabriela N. ^[1]
  1. [1] Universidad de Concepción

     Universidad de Concepción

     Comuna de Concepción, Chile

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 13, Nº. 2, 1994, págs. 63-84
• Idioma: inglés
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• Resumen

  • 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.