Superconvergence in the Generalized Finite Element Method
Abstract
In this paper, we address the problem of the existence of superconvergence points of approximate solutions, obtained from the Generalized Finite Element Method (GFEM), of a Neumann elliptic boundary value problem. GFEM is a Galerkin method that uses non-polynomial shape functions. In particular, we show that the superconvergence points for the gradient of the approximate are zeros of certain systems of non-linear equations that do not depend on the solution of the boundary value problem. For approximate solutions with second derivatives, we have also characterized the superconvergence points of the second derivatives of the approximate solution as the roots of certain systems of non-linear equations. We note that it is easy to construct smooth generalized finite element approximation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2005
- Accession Number
- ADA440610
Entities
People
- Ivo Babuška
- John E. Osborn
- Uday Banerjee
Organizations
- University of Texas at Austin