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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

4 Issues per year

IMPACT FACTOR 2016: 1.097

CiteScore 2016: 1.09

SCImago Journal Rank (SJR) 2016: 0.872
Source Normalized Impact per Paper (SNIP) 2016: 0.887

Mathematical Citation Quotient (MCQ) 2016: 0.75

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Volume 14, Issue 2


Goal-Oriented Error Estimation for the Fractional Step Theta Scheme

Dominik Meidner / Thomas Richter
Published Online: 2014-01-16 | DOI: https://doi.org/10.1515/cmam-2014-0002


In this work, we derive a goal-oriented a posteriori error estimator for the error due to time-discretization of nonlinear parabolic partial differential equations by the fractional step theta method. This time-stepping scheme is assembled by three steps of the general theta method, that also unifies simple schemes like forward and backward Euler as well as the Crank–Nicolson method. Further, by combining three substeps of the theta time-stepping scheme, the fractional step theta time-stepping scheme is derived. It possesses highly desired stability and numerical dissipation properties and is second order accurate. The derived error estimator is based on a Petrov–Galerkin formulation that is up to a numerical quadrature error equivalent to the theta time-stepping scheme. The error estimator is assembled as one weighted residual term given by the dual weighted residual method and one additional residual estimating the Galerkin error between time-stepping scheme and Petrov–Galerkin formulation.

Keywords: Nonlinear Parabolic Systems; Petrov–Galerkin Schemes; A Posteriori Error Estimation

MSC: 65M60; 65L60; 65L70; 65M15

About the article

Published Online: 2014-01-16

Published in Print: 2014-04-01

Citation Information: Computational Methods in Applied Mathematics, Volume 14, Issue 2, Pages 203–230, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2014-0002.

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© 2014 by Walter de Gruyter Berlin/Boston. Copyright Clearance Center

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