Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Finite element approximation of the $ p$-Laplacian


Authors: John W. Barrett and W. B. Liu
Journal: Math. Comp. 61 (1993), 523-537
MSC: Primary 65N30
MathSciNet review: 1192966
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we consider the continuous piecewise linear finite element approximation of the following problem: Given $ p \in (1,\infty )$, f, and g, find u such that

$\displaystyle - \nabla \cdot (\vert\nabla u{\vert^{p - 2}}\nabla u) = f\quad {\... ...\;\Omega \subset {\mathbb{R}^2},\quad u = g\quad {\text{on}}\;\partial \Omega .$

The finite element approximation is defined over $ {\Omega ^h}$, a union of regular triangles, yielding a polygonal approximation to $ \Omega $. For sufficiently regular solutions u, achievable for a subclass of data f, g, and $ \Omega $, we prove optimal error bounds for this approximation in the norm $ {W^{1,q}}({\Omega ^h}),q = p$ for $ p < 2$ and $ q \in [1,2]$ for $ p > 2$, under the additional assumption that $ {\Omega ^h} \subseteq \Omega $. Numerical results demonstrating these bounds are also presented.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N30

Retrieve articles in all journals with MSC: 65N30


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1993-1192966-4
PII: S 0025-5718(1993)1192966-4
Article copyright: © Copyright 1993 American Mathematical Society