Elliptic Reconstruction and a Posteriori Error Estimates for Parabolic Problems
نویسندگان
چکیده
منابع مشابه
Elliptic Reconstruction and a Posteriori Error Estimates for Parabolic Problems
It is known that the energy technique for a posteriori error analysis of finite element discretizations of parabolic problems yields suboptimal rates in the norm L∞(0, T ; L2(Ω)). In this paper we combine energy techniques with an appropriate pointwise representation of the error based on an elliptic reconstruction operator which restores the optimal order (and regularity for piecewise polynomi...
متن کاملElliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems
We derive a posteriori error estimates for fully discrete approximations to solutions of linear parabolic equations. The space discretization uses finite element spaces that are allowed to change in time. Our main tool is an appropriate adaptation of the elliptic reconstruction technique, introduced by Makridakis and Nochetto. We derive novel a posteriori estimates for the norms of L∞(0, T ; L2...
متن کاملA Posteriori Error Estimates for Parabolic Problems via Elliptic Reconstruction and Duality
We use the elliptic reconstruction technique in combination with a duality approach to prove a posteriori error estimates for fully discrete backward Euler scheme for linear parabolic equations. As an application, we combine our result with the residual based estimators from the a posteriori estimation for elliptic problems to derive space-error estimators and thus a fully practical version of ...
متن کاملSharply local pointwise a posteriori error estimates for parabolic problems
We prove pointwise a posteriori error estimates for semiand fullydiscrete finite element methods for approximating the solution u to a parabolic model problem. Our estimates may be used to bound the finite element error ‖u−uh‖L∞(D), where D is an arbitrary subset of the space-time domain of definition of the given PDE. In contrast to standard global error estimates, these estimators de-emphasiz...
متن کاملResidual type a posteriori error estimates for elliptic obstacle problems
under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we give an a posteriori error estimates with constitutive law for some obstacle problem. The error estimator involves some parameter ε appeared in some penalized equation.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2003
ISSN: 0036-1429,1095-7170
DOI: 10.1137/s0036142902406314