| dc.description.abstract | the finite element solution of certain two-point boundary value
problems is discussed.
in order to obtain more accuracy than the linear finite element
method can give, an order-h[superscript 4] global superconvergence technique is studied. this technique, which uses a quasi-inverse of the rayleigh-ritz-galerkin (finite element) method, is motivated by the papers of
c. de boor and g. j. fix [14] and p. 0. frederickson [25]. the
peano kernel theorem is generalized and used to approximate the rate
of convergence of the global superconvergence.
following sard’s theory on best quadrature formulae [50], with
some generalization, several quadrature formulae are derived. these
quadrature formulae are shown to be consistent, and have some advantages
over those obtained by herbold, schultz and varga [34].
for solution of large linear systems which result from the finite
element method, lu decomposition (gaussian elimination method) is fast
and accurate. however, when it comes to a singular or a nearly singular
system, lu decomposition fails. the algorithm fapin developed by
p. 0. frederickson for 2-dimensional systems is able to solve singular
systems as we demonstrate.
we found fapin will work more efficiently in 1-dimensional case
if we replace the db[subscript q] approximate inverse c, developed by benson [3],
with other approximate inverses.
for the sake of verifying the theory, appropriate numerical
experiments are carried out. | |
