Summary: A POSTERIORI FINITE ELEMENT ERROR
SECOND-ORDER HYPERBOLIC PROBLEMS
Department of Mathematics
Interdisciplinary Center for Applied Mathematics
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061
March 7, 2002
We develop a posteriori finite element discretization error estimates for the
wave equation. In one dimension, we show that the significant part of the spatial
finite element error is proportional to a Lobatto polynomial and an error estimate
is obtained by solving a set of either local elliptic or hyperbolic problems. In
two dimensions, we show that the dichotomy principle of Babuska and Yu holds.
For even-degree approximations error estimates are computed by solving a set of
local elliptic or hyperbolic problems and for odd-degree approximations an error
estimate is computed using jumps of solution gradients across element boundaries.
This study also extends known superconvergence results for elliptic and parabolic