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SIAMNUM
2010
129views more  SIAMNUM 2010»
12 years 10 months ago
Convergence of an Adaptive Finite Element Method for Controlling Local Energy Errors
A number of works concerning rigorous convergence theory for adaptive finite element methods (AFEM) for controlling global energy errors have appeared in recent years. However, man...
Alan Demlow
MOC
2000
127views more  MOC 2000»
13 years 3 months ago
Can a finite element method perform arbitrarily badly?
In this paper we construct elliptic boundary value problems whose standard finite element approximations converge arbitrarily slowly in the energy norm, and show that adaptive proc...
Ivo Babuska, John E. Osborn
SIAMNUM
2010
150views more  SIAMNUM 2010»
12 years 10 months ago
Quasi-Optimal Convergence Rate of an Adaptive Discontinuous Galerkin Method
We analyze an adaptive discontinuous finite element method (ADFEM) for symmetric second order linear elliptic operators. The method is formulated on nonconforming meshes made of si...
Andrea Bonito, Ricardo H. Nochetto
MOC
2002
81views more  MOC 2002»
13 years 3 months ago
Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection--diffusion problem
We study the convergence properties of the hp-version of the local discontinuous Galerkin finite element method for convection-diffusion problems; we consider a model problem in a ...
Paul Castillo, Bernardo Cockburn, Dominik Schö...
MOC
2011
12 years 10 months ago
Local energy estimates for the finite element method on sharply varying grids
Abstract. Local energy error estimates for the finite element method for elliptic problems were originally proved in 1974 by Nitsche and Schatz. These estimates show that the loca...
Alan Demlow, Johnny Guzmán, Alfred H. Schat...