911 research outputs found
Adaptive Numerical Methods for PDEs
This collection contains the extended abstracts of the talks given at the Oberwolfach Conference on “Adaptive Numerical Methods for PDEs”, June 10th - June 16th, 2007. These talks covered various aspects of a posteriori error estimation and mesh as well as model adaptation in solving partial differential equations. The topics ranged from the theoretical convergence analysis of self-adaptive methods, over the derivation of a posteriori error estimates for the finite element Galerkin discretization of various types of problems to the practical implementation and application of adaptive methods
A posteriori error estimates in the maximum norm for parabolic problems
We derive a posteriori error estimates in the
norm for approximations of solutions to
linear para bolic equations. Using the elliptic reconstruction technique
introduced by Makridakis and Nochetto and heat kernel estimates for linear
parabolic pr oblems, we first prove a posteriori bounds in the maximum norm for
semidiscrete finite element approximations. We then establish a posteriori
bounds for a fully discrete backward Euler finite element approximation. The
elliptic reconstruction technique greatly simplifies our development by allow\
ing the straightforward combination of heat kernel estimates with existing
elliptic maximum norm error estimators
Improved ZZ A Posteriori Error Estimators for Diffusion Problems: Conforming Linear Elements
In \cite{CaZh:09}, we introduced and analyzed an improved Zienkiewicz-Zhu
(ZZ) estimator for the conforming linear finite element approximation to
elliptic interface problems. The estimator is based on the piecewise "constant"
flux recovery in the conforming finite element space. This
paper extends the results of \cite{CaZh:09} to diffusion problems with full
diffusion tensor and to the flux recovery both in piecewise constant and
piecewise linear space.Comment: arXiv admin note: substantial text overlap with arXiv:1407.437
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