Bq. Guo et Wm. Cao, ADDITIVE SCHWARZ METHODS FOR THE H-P VERSION OF THE FINITE-ELEMENT METHOD IN 2 DIMENSIONS, SIAM journal on scientific computing, 18(5), 1997, pp. 1267-1288
Two additive Schwarz methods (ASMs) are proposed for the h-p version o
f the finite element method for two-dimensional elliptic problems in p
olygonal domains. One is based on generous overlapping of the h-versio
n components (i.e., the linear nodal modes) and nonoverlapping of the
p-version components (i.e., the high-order side modes and internal mod
es). Another is based on nonoverlapping for both the h-version and the
p-version components. Their implementations are in parallel on the su
bdomain level for the h-version components and on the element level fo
r the p-version components. The condition number for the first method
is of order O(1 + ln p)(2), and for the second one is max(i)(1 + ln(H(
i)p(i)/h(i)))(2), where H-i is the diameter of the subdomain Omega(i),
h(i) is the characteristic diameter of the elements in Omega(i), p(i)
is the maximum polynomial degree used in Omega(i), and p = max(i)p(i)
.