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Quasi-norm error bounds for the finite element approximation of some degenerate quasilinear parabolic equations and variational inequalities

Liu, Wenbin, Barrett, John W. (1995) Quasi-norm error bounds for the finite element approximation of some degenerate quasilinear parabolic equations and variational inequalities. Numerical Functional Analysis and Optimization, 16 (9-10). pp. 1309-1321. ISSN 0163-0563. (doi:10.1080/01630569508816675) (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) (KAR id:37138)

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/10.1080/01630569508816675

Abstract

In this paper we study the continuous piecewise linear finite element approximation of the following problem:

Let ? be an open set in Rd with d=l or 2. Given T>0, f and uO; find u?K, where K is a closed convex subset of the So bo lev space , such that for x?? and for any v?K

for a.e. t?(0,T], where k?C(0,?) is a given nonnegative function with k(s)s strictly increasing for s?O, but possibly degenerate, and p?(1,?) depends on k.

For such a general problem we establish error bounds in energy type norms for a fully discrete approximation based on the backward Euler time discretisation. We show that these error bounds converge at the optimal rate with respect to the space discretisation, provided p?2 and the solution u is sufficiently regular.

Item Type: Article
DOI/Identification number: 10.1080/01630569508816675
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Social Sciences > Kent Business School
Depositing User: Steve Liu
Date Deposited: 02 Dec 2013 16:57 UTC
Last Modified: 06 May 2020 03:09 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/37138 (The current URI for this page, for reference purposes)
Liu, Wenbin: https://orcid.org/0000-0001-5966-6235
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