부산대학교 도서관

The authors apply an adaptive finite element method to the computationof disc type minimal surfaces. This work builds on previous work byG. 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 methodsapply to stationary surfaces that are not minimizers.\parCrucial to the authors' work are the a posteriori error estimates ofTheorems 4.9 and 4.11. These results are too complicated to describehere. The bounding terms in these estimates are not, in fact, fullycomputable, so the authors provide additional heuristics for apractical algorithm.\parThe authors apply the algorithm to Enneper's surface and to curvesthat wind around the torus.