Adaptive Crank-Nicolson methods with dynamic finite-element spaces for parabolic problems

Dongho Kim, Eun Jae Park

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We construct a posteriori error estimators for approximate solutions of linear parabolic equations. We consider discretizations of the problem by modified discontinuous Galerkin schemes in time and continuous Galerkin methods in space. Especially, finite element spaces are permitted to change at different time levels. Exploiting Crank-Nicolson reconstruction idea introduced by Akrivis, Makridakis & Nochetto [2], we derive space-time a posteriori error estimators of second order in time for the Crank-Nicolson-Galerkin finite element method.

Original languageEnglish
Pages (from-to)873-886
Number of pages14
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume10
Issue number4
Publication statusPublished - 2008 Nov 1

Fingerprint

Crank-Nicolson Method
Adaptive Method
Parabolic Problems
Crank-Nicolson
A Posteriori Error Estimators
Finite Element
Galerkin methods
Galerkin Finite Element Method
Discontinuous Galerkin
Galerkin Method
Finite element method
Parabolic Equation
Linear equation
Approximate Solution
Discretization
Space-time

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

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Adaptive Crank-Nicolson methods with dynamic finite-element spaces for parabolic problems. / Kim, Dongho; Park, Eun Jae.

In: Discrete and Continuous Dynamical Systems - Series B, Vol. 10, No. 4, 01.11.2008, p. 873-886.

Research output: Contribution to journalArticle

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