ISSN:
0945-3245
Keywords:
AMS(MOS): G5N30
;
CR: G1.8
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Given λ〉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⊂ℝ2 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01385777
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