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

Dongho Kim; Eun Jae Park

doi:10.3934/dcdsb.2008.10.873

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

Dongho Kim, Eun Jae Park

Department of Computational Science and Engineering

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	873-886
Number of pages	14
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	10
Issue number	4
DOIs	https://doi.org/10.3934/dcdsb.2008.10.873
Publication status	Published - 2008 Nov

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.3934/dcdsb.2008.10.873

Fingerprint Dive into the research topics of 'Adaptive Crank-Nicolson methods with dynamic finite-element spaces for parabolic problems'. Together they form a unique fingerprint.

Cite this

@article{3ef962bb58a640b19ab076f60581caf3,

title = "Adaptive Crank-Nicolson methods with dynamic finite-element spaces for parabolic problems",

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.",

author = "Dongho Kim and Park, {Eun Jae}",

year = "2008",

month = nov,

doi = "10.3934/dcdsb.2008.10.873",

language = "English",

volume = "10",

pages = "873--886",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "Southwest Missouri State University",

number = "4",

}

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

Y1 - 2008/11

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.

UR - http://www.scopus.com/inward/record.url?scp=57749202892&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57749202892&partnerID=8YFLogxK

U2 - 10.3934/dcdsb.2008.10.873

DO - 10.3934/dcdsb.2008.10.873

M3 - Article

AN - SCOPUS:57749202892

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 -