Generalized topological efficiency – case study with C84 fullerene
AbstractA pure topological mechanism able to explain fullerenes stability is presented here. The non-trivial case of the C84 fullerene isomers with isolated Pentagons Is in fact analyzed. This orig...
Given ?>0 andp?(0,1), we consider the following problem: findu such that $$\begin{gathered} - \Delta u + \lambda [u]_ + ^p = 0in\Omega , \hfill \\ u = 1on\partial \Omega , \hfill \\ \end{gathered} $$ whereΩ??2 is a smooth convex domain. We prove optimalH 1 andL ? error bounds for the standard continuous piecewise linear Galerkin finite element approximation. In addition we analyse a more practical approximation using numerical integration on the nonlinear term. Finally we consider a modified nonlinear SOR algorithm, which is shown to be globally convergent, for solving the algebraic system derived from the more practical approximation.