Paper Info
Title
Linear finite elements may be only first-order pointwise accurate on anisotropic triangulations.
Abstract
We give a counterexample of an anisotropic triangulation on which the exact solution has a second-order error of linear interpolation, while the computed solution obtained using linear finite elements is only first-order pointwise accurate. Our example is given in the context of a singularly perturbed reaction-diffusion equation, whose exact solution exhibits a sharp boundary layer. Furthermore, we give a theoretical justification of the observed numerical phenomena using a finite-difference representation of the considered finite element methods. Both standard and lumped-mass cases are addressed.
Year
DOI
Venue
2014
10.1090/S0025-5718-2014-02820-2
MATHEMATICS OF COMPUTATION
Keywords
Field
DocType
Anisotropic triangulation,linear finite elements,maximum norm,singular perturbation,Bakhvalov mesh,Shishkin mesh
Exact solutions in general relativity,Mathematical optimization,Mathematical analysis,Finite element method,Singular perturbation,Triangulation (social science),Boundary layer,Linear interpolation,Counterexample,Mathematics,Pointwise
Journal
Volume
Issue
ISSN
83
289
0025-5718
Citations 
PageRank 
References 
0
0.34
3
Authors
1
Name
Order
Citations
PageRank
Natalia Kopteva113022.08