Paper Info
Title
Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEM
Abstract
Averaging techniques are popular tools in adaptive finite element methods since they provide efficient a posteriori error estimates by a simple postprocessing. In the second paper of our analysis of their reliability, we consider conforming h-FEM of higher (i.e., not of lowest) order in two or three space dimensions. In this paper, reliablility is shown for conforming higher order finite element methods in a model situation, the Laplace equation with mixed boundary conditions. Emphasis is on possibly unstructured grids, non-smoothness of exact solutions, and a wide class of local averaging techniques. Theoretical and numerical evidence supports that the reliability is up to the smoothness of given right-hand sides.
Year
DOI
Venue
2002
10.1090/S0025-5718-02-01412-6
MATHEMATICS OF COMPUTATION
Keywords
Field
DocType
a posteriori error estimates,residual based error estimate,adaptive algorithm,reliability,finite element method,higher order finite element method
Boundary value problem,Mathematical optimization,Mathematical analysis,A priori and a posteriori,Finite element method,Laplace's equation,Adaptive algorithm,Smoothness,Partial differential equation,Elliptic curve,Mathematics
Journal
Volume
Issue
ISSN
71
239
0025-5718
Citations 
PageRank 
References 
16
5.55
2
Authors
2
Name
Order
Citations
PageRank
Sören Bartels135556.90
C Carstensen2944163.02