Adaptive Multilevel-Methods in 3-Space Dimensions.
Appeared in: International Journal for Numerical Methods in Engineering, Vol. 36, pp. 3187-3203 (1993)
| SC 92-14 | Folkmar A. Bornemann, Bodo Erdmann, Ralf Kornhuber
Adaptive Multilevel-Methods in 3-Space Dimensions. Appeared in: International Journal for Numerical Methods in Engineering, Vol. 36, pp. 3187-3203 (1993) | |
Abstract: We consider the approximate solution of
selfadjoint elliptic problems in three space dimensions by
piecewise linear finite elements with respect to a highly
non-uniform tetrahedral mesh which is generated adaptively.
The arising linear systems are solved iteratively by the
conjugate gradient method provided with a multilevel
preconditioner. Here, the accuracy of the iterative solution
is coupled with the discretization error. as the performance
of hierarchical bases preconditioners deteriorate in three
space dimensions, the BPX preconditioner is used, taking
special care of an efficient implementation. Reliable
a-posteriori estimates for the discretization error are
derived from a local comparison with the approximation
resulting from piecewise quadratic elements. To illustrate
the theoretical results, we consider a familiar model
problem involving reentrant corners and a real-life problem
arising from hyperthermia, a recent clinical method for
cancer therapy.