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 language | English |
|---|---|
| Pages (from-to) | 873-886 |
| Number of pages | 14 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 10 |
| Issue number | 4 |
| Publication status | Published - 2008 Nov 1 |
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All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics
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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 journal › Article
TY - JOUR
T1 - Adaptive Crank-Nicolson methods with dynamic finite-element spaces for parabolic problems
AU - Kim, Dongho
AU - Park, Eun Jae
PY - 2008/11/1
Y1 - 2008/11/1
N2 - 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.
AB - 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.
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M3 - Article
VL - 10
SP - 873
EP - 886
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
SN - 1531-3492
IS - 4
ER -