Annual progress report, FY1974 Page: 14 of 38
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11.
problems, the finite element method should provide accurate
solutions with fewer unknowns than is characterized by the
usual finite difference approximations used in reactor physics
analysis. In the past we have studied the application of
finite element methods to problems in two-dimensional reactors
with properties characteristic of contemporary power reactors.
In addition, much of the work has been of a theoretical nature
dealing with the selection of element functions, proof of
error bounds, rates of convergence and the like. In the past
year we have concentrated on two problems: The first of which has
to do with the degree of smoothness one can assume in the
spatial solution and still obtain reasonable accuracy. The
second problem has to .do with the choice of basis function used
with hexagonal geometries.
Some of the work discussed in previous reports has indicated
that it is acceptable to use interface conditions for finite
element methods involving continuity of derivitive rather than
continuity of current. This implies that the finite element
solution is smoother in space than the actual solution to the
physical problem. However, the virtue of having a smooth
solution is the rapid convergence. Some preliminary results
dealing with PWR assemblies have indicated that it is reasonable
to expect accurate solutions when one uses derivitive continuity,
provided the material properties are not too different from
one assembly to the next. As a practical matter, the results
indicated excellent agreement with accurate finite difference
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Hansen, K. F. & Henry, A. F. Annual progress report, FY1974, report, April 1974; Cambridge, Massachusetts. (https://digital.library.unt.edu/ark:/67531/metadc1019464/m1/14/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.