Construction of basic functions for numerical utilisation of Ritz's method

Approximation by finite element functions using local regularization

“…A is a closed bounded two-dimensional domain with polygonal boundary For spécifie examples see [2], [3], [4], [5], [6], [7]. we shall prove :…”

“…The mathematical problem of approximation by finite element functions has been first studied by Goël ( [2]) and Zlamal ([3]). In [4], Bramble and Zlamal give estimâtes for the error in terms of Sobolev norms, however their results are based on the existence and continuity of the interpolate ; but the interpolate may not exist; for example if u e H l (Q) where Qis a two-dimensional domain, by Sobolev's imbedding theorem, the pointwise values of u cannot be defined and consequently no interpolation is possible.…”

A Curved Finite Element for Thin Elastic Shells

“…This remark has been confirmed theoretically in [16]. Contrary to what has occasionally been stated in the literature, the condition that rigid-body motions should be properly represented is essential, not for convergence in energy [17], but for acceptable rate of convergence. If this condition is fulfilled, it can show that the stresses and reactions computed from the approximate displacements assure the equilibrium of the shell , and this is, of course, of great practical importance.…”

Solution of Multi-Dimensional Neutron Transport Equation by Finite Element Method

“…Now our scheme can be obtained from Eq. (13) by assuming that u is of the form of Eq. (14), and by restricting the trial functions to Vh.…”