Publication Date:
2011-11-24
Description:
In this paper we consider the finite-volume-element method for general second-order quasilinear elliptic problems over a convex polygonal domain in the plane. Using reasonable assumptions, we show the existence and uniqueness of the finite-volume-element approximations. It is proved that the finite-volume-element approximations are convergent with , where r 〉 2, and in the H 1 -, W 1, - and L 2 -norms, respectively, for u W 2, r () and u W 2, () W 3, p (), where p 〉 1. Moreover, the optimal-order error estimates in the W 1, - and L 2 -norms and an estimate in the L -norm are derived under the assumption that u W 2, () H 3 (). Numerical experiments are presented to confirm the estimates.
Print ISSN:
0272-4979
Electronic ISSN:
1464-3642
Topics:
Mathematics
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