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Finite element approximation of some degenerate monotone quasilinear elliptic systems

Liu, Wenbin, Barrett, John W. (1996) Finite element approximation of some degenerate monotone quasilinear elliptic systems. SIAM Journal on Numerical Analysis, 33 (1). pp. 88-106. ISSN 0036-1429. (doi:10.1137/0733006) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1137/0733006

Abstract

In this paper we examine the continuous piecewise linear finite element approximation of the following system: given f ? (fj) and g = (gj), find u = (uj) (j = 1 ? r with r = 1 or 2) such that -?.(K(z, ?u(z))?u(z)) = f(z), z ? ? ?R2, u|?? = g|??, where (?u)ij = ?uj/?zi 1 ? ? 2, 1 ? j ? r and K is a given matrix on ? x R2xr. We characterize a class of matrices K for which we prove error bounds for this discretization. For sufficiently regular solutions u, achievable at least for some model problems, our bounds improve on existing results in the literature. It is shown that for a notable subclass of K, for which only suboptimal error bounds have been previously derived, the piecewise linear finite element approximation of this problem will converge at the optimal rate in an energy-type norm. It is also shown that the techniques used in this paper can be applied to more general problems.

Item Type: Article
DOI/Identification number: 10.1137/0733006
Uncontrolled keywords: Degenerate elliptic systems, Error analysis, Finite elements
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Divisions: Faculties > Social Sciences > Kent Business School > Management Science
Depositing User: Steve Wenbin Liu
Date Deposited: 27 Nov 2013 09:43 UTC
Last Modified: 29 May 2019 11:28 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/36850 (The current URI for this page, for reference purposes)
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