부산대학교 도서관

The authors apply an adaptive finite element method to the computation of disc type minimal surfaces. This work builds on previous work by G. Dziuk and J. E. Hutchinson [Calc. Var. Partial Differential Equations {\bf 4} (1996), no.~1, 27--58; MR1379192 (96m:49073); Math. Comp. {\bf 68} (1999), no.~225, 1--23; MR1613695 (2000a:65144); Math. Comp. {\bf 68} (1999), no.~226, 519--546; MR1613699 (2000a:65145)]. An important feature is that the methods apply to stationary surfaces that are not minimizers. \par Crucial to the authors' work are the a posteriori error estimates of Theorems 4.9 and 4.11. These results are too complicated to describe here. The bounding terms in these estimates are not, in fact, fully computable, so the authors provide additional heuristics for a practical algorithm. \par The authors apply the algorithm to Enneper's surface and to curves that wind around the torus.