Paper Info
Title
Global Superconvergence and A Posteriori Error Estimators of the Finite Element Method for a Quasi-linear Elliptic Boundary Value Problem of Nonmonotone Type
Abstract
In this paper we are concerned with finite element approximations to a nonlinear elliptic partial differential equation with homogeneous Dirichlet boundary conditions. This kind of problems arises for example from modeling a stationary heat conduction in nonlinear inhomogeneous and anisotropic media. For finite elements of degree k \geq 1 in each variable, by means of an interpolation postprocessing technique, we obtain the global superconvergence of O(hk + 1) in the H1-norm and O(hk + 2) in the L2-norm provided the weak solution is sufficiently smooth. As by-products, the global superconvergence results can be used to generate efficient a posteriori error estimators. Representative numerical examples are also given to illustrate our theoretical analysis.
Year
DOI
Venue
2004
10.1137/S0036142903428402
SIAM J. Numerical Analysis
Keywords
Field
DocType
anisotropic media,global superconvergence,global superconvergence result,finite element approximation,nonlinear elliptic partial differential,nonmonotone type,finite element,nonlinear inhomogeneous,degree k,interpolation postprocessing technique,finite element method,homogeneous dirichlet boundary condition,quasi-linear elliptic boundary value,posteriori error estimators,elliptic boundary value problem,finite elements
Boundary value problem,Mathematical optimization,Mathematical analysis,Dirichlet boundary condition,Superconvergence,Finite element method,Numerical analysis,Elliptic partial differential equation,Partial differential equation,Mathematics,Elliptic boundary value problem
Journal
Volume
Issue
ISSN
42
4
0036-1429
Citations 
PageRank 
References 
5
0.45
0
Authors
5
Name
Order
Citations
PageRank
Liping Liu122212.32
Tang Liu28011.28
Michal Křížek39115.53
Tao Lin415321.03
Shuhua Zhang5389.06