Data oscillation and convergence of adaptive FEM

SIAM J. Numer. Anal., 38, 2 (2000), 466-488.

Pedro Morin
Department of Mathematics
University of Maryland, College Park
College Park, MD 20742, USA

pmorin@math.umd.edu

Ricardo H. Nochetto
Department of Mathematics
University of Maryland, College Park
College Park, MD 20742, USA

rhn@math.umd.edu

Kunibert G.\ Siebert
Institut f\"ur Angewandte Mathematik
Hermann-Herder-Str.\ 10
79104 Freiburg, Germany

kunibert@mathematik.uni-freiburg.de

Abstract

Data oscillation is intrinsic information missed by the averaging process associated with finite element methods (FEM) regardless of quadrature. Ensuring a reduction rate of data oscillation, together with an error reduction based on a posteriori error estimators, we construct a simple and efficient adaptive FEM for elliptic PDE with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants. Any prescribed error tolerance is thus achieved in a finite number of steps. A number of numerical experiments in 2d and 3d yield quasi-optimal meshes along with a competitive performance.