An efficient direct solver for the boundary concentrated FEM in 2D

  • Authors:
  • B. N. Khoromskij;J. M. Melenk

  • Affiliations:
  • Max-Planck-Institute for Mathematics in the Sciences, Inselstraße. 22-26, D-04103 Leipzig, Germany;Max-Planck-Institute for Mathematics in the Sciences, Inselstraße. 22-26, D-04103 Leipzig, Germany

  • Venue:
  • Computing
  • Year:
  • 2002

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Abstract

The boundary concentrated FEM, a variant of the hp-version of the finite element method, is proposed for the numerical treatment of elliptic boundary value problems. It is particularly suited for equations with smooth coefficients and non-smooth boundary conditions. In the two-dimensional case it is shown that the Cholesky factorization of the resulting stiffness matrix requires O(Nlog4N) units of storage and can be computed with O(Nlog8N) work, where N denotes the problem size. Numerical results confirm theoretical estimates.