ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991):65N30, 65N15
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. Given $ \nu \in{\Bbb R}_{+} $ , we consider the following problem: find $u 〉 0$ , such that \begin{displaymath} -\Delta u = cu^{-\nu} \quad \mbox{in}\,\, \Omega\,, \quad u = 0 \quad \mbox{on}\,\, \partial \Omega\,, \end{displaymath} where $\Omega \subset{\Bbb R}^{d},\, d = 1,\,2$ or 3, and $c 〉 0$ in $\bar{\Omega}$ . We prove $H^{1}$ and $L^{\infty}$ error bounds for the standard continuous piecewise linear Galerkin finite element approximation with a (weakly) acute triangulation. Our bounds are nearly optimal. In addition, for d = 1 and 2 and $c \in{\Bbb R}_{+}$ we analyze a more practical scheme involving numerical integration on the nonlinear term. We obtain nearly optimal $H^{1}$ and $L^{\infty}$ error bounds for d = 1. For this case we also present some numerical results.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050410
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