A Hermitian Box-scheme for One-dimensional Elliptic Equations – Application to Problems with High Contrasts in the Ellipticity

  • Authors:

  • J.-P. Croisille

  • Affiliations:

  • Laboratoire Mathématiques et Applications de Metz, UMR 7122, Université de Metz, 57045, Metz Cedex, Ile du Saulcy, Metz, France

  • Venue:
  • Computing
  • Year:
  • 2006

Quantified Score

Hi-index 0.00

Visualization

Abstract

We introduce a new box-scheme, called ``hermitian box-scheme'' on the model of the one-dimensional Poisson problem. The scheme combines features of the box-scheme of Keller, [20], [13], with the hermitian approximation of the gradient on a compact stencil, which is characteristic of compact schemes, [9], [21]. The resulting scheme is proved to be 4th order accurate for the primitive unknown u and its gradient p. The proved convergence rate is 1.5 for (u,p) in the discrete L2 norm. The connection with a non standard mixed finite element method is given. Finally, numerical results are displayed on pertinent 1-D elliptic problems with high contrasts in the ellipticity, showing in practice convergence rates ranging from 1 to 2.5 in the discrete H1 norm.