Premium
The treatment of natural boundary conditions in the finite element and finite difference methods
Author(s) -
Croll J. G. A.
Publication year - 1973
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620050312
Subject(s) - finite element method , boundary knot method , boundary value problem , mathematics , extended finite element method , mixed finite element method , finite difference method , mathematical analysis , boundary (topology) , finite difference , representation (politics) , boundary element method , structural engineering , engineering , politics , political science , law
To isolate the relative accuracy in the numerical approximation of the natural boundary conditions, a plane‐ stress example is presented for which the field equations using finite element and finite difference methods are identical. For this example, and by implication a wider class of problem, it is demonstrated that by using conventional practice in both methods the implicit representation of the natural boundary conditions in the finite element gives rise to a lower numerical accuracy than that in the less convenient explicit satisfaction of these boundary conditions in finite difference method.