Location of Repository

A posteriori error control for fully discrete Crank–Nicolson schemes

By E Bänsch, F Karakatsani and C Makridakis

Abstract

We derive residual-based a posteriori error estimates of optimal order for fully discrete approximations for linear parabolic problems. The time discretization uses the Crank--Nicolson method, and the space discretization uses finite element spaces that are allowed to change in time. The main tool in our analysis is the comparison with an appropriate reconstruction of the discrete solution, which is introduced in the present paper

Topics: QA297
Publisher: Society for Industrial and Applied Mathematics
Year: 2012
OAI identifier: oai:sro.sussex.ac.uk:44784

Suggested articles

Preview

Citations

  1. (2003). A posteriori error estimates for finite element discretizations of the heat equation, doi
  2. (2006). A posteriori error estimates for the Crank-Nicolson method for parabolic equations, doi
  3. (2000). A Posteriori Error Estimation in Finite Element Analysis, Wiley-Interscience, doi
  4. (1996). A time- and space-adaptive algorithm for the linear time-dependent Schr¨ odinger equation,
  5. (2004). Adaptive Computational Methods for Parabolic Problems, doi
  6. (1991). Adaptive finite element methods for parabolic problems I:A linear model problem, doi
  7. (1990). An a posteriori error estimate and adaptive timestep control for a backward Euler discretization of a parabolic problem,S I A MJ .N u m e r .A n a l . doi
  8. (2009). An anisotropic error estimator for the Crank–Nicolson method: Application to a parabolic problem, doi
  9. (2006). Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems, doi
  10. (2003). Elliptic reconstruction and a posteriori error estimates for parabolic problems, doi
  11. (2000). Estimating the error of numerical solutions of systems of reaction-diffusion equations, doi
  12. (1990). Finite element interpolation of nonsmooth functions satisfying boundary conditions, doi
  13. (1997). Galerkin Finite Element Methods for Parabolic Problems, doi
  14. (1982). On the smoothing property of the Crank-Nicolson scheme, doi
  15. (2007). Space and time reconstructions in a posteriori analysis of evolution problems, doi
  16. (2009). Space-Time Adaptive Algorithms for Parabolic problems: A Posteriori Error Estimates and Application to Microfluidics,
  17. (2009). Unauthorized reproduction of this article is prohibited.
  18. (1996). Verf¨ urth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.