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Russian Journal of Numerical Analysis and Mathematical Modelling

Editor-in-Chief: Dymnikov, Valentin P. / Kuznetsov, Yuri

Managing Editor: Vassilevski, Yuri V.

Editorial Board: Agoshkov, Valeri I. / Amosov, Andrey A. / Kaporin, Igor E. / Kobelkov, Georgy M. / Mikhailov, Gennady A. / Repin, Sergey I. / Shaidurov, Vladimir V. / Shokin, Yuri I. / Tyrtyshnikov, Eugene E.


IMPACT FACTOR 2018: 0.779

CiteScore 2018: 0.92

SCImago Journal Rank (SJR) 2018: 0.512
Source Normalized Impact per Paper (SNIP) 2018: 1.275

Mathematical Citation Quotient (MCQ) 2017: 0.13

Online
ISSN
1569-3988
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Volume 30, Issue 6

Issues

High order approximations in space and time of a sixth order Cahn–Hilliard equation

Oleg Boyarkin / Ronald H. W. Hoppe
  • Corresponding author
  • Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA
  • Institute of Mathematics, University of Augsburg, D-86159 Augsburg, Germany. E-mail: hoppe@math.uni-augsburg.de
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/ Christopher Linsenmann
Published Online: 2015-12-08 | DOI: https://doi.org/10.1515/rnam-2015-0029

Abstract

We consider an initial-boundary value problem for a sixth order Cahn-Hilliard equation describing the formation of microemulsions. Based on a Ciarlet-Raviart type mixed formulation as a system consisting of a second order and a fourth order equation, the spatial discretization is done by a C0 Interior Penalty Discontinuous Galerkin (C0IPDG) approximation with respect to a geometrically conforming simplicial triangulation of the computational domain. The DG trial spaces are constructed by C0 conforming Lagrangian finite elements of polynomial degree k ≥ 2. This leads to an initial value problem for an index 1 Differential Algebraic Equation (DAE) which is further discretized in time by an s-stage Diagonally Implicit Runge-Kutta (DIRK) method of order p ≥ 2. The resulting parameter dependent nonlinear algebraic system is solved numerically by a predictor-corrector continuation strategy with constant continuation as a predictor and New- ton’s method as a corrector featuring an adaptive choice of the continuation parameter. Numerical results illustrate the performance of the suggested approach.

Keywords : Sixth order Cahn-Hilliard equation; interior penalty discontinuous Galerkin methods; diagonally implicit Runge-Kutta methods; automatic step-size selection in time

About the article

Received: 2015-09-25

Accepted: 2015-10-15

Published Online: 2015-12-08

Published in Print: 2015-12-01


Citation Information: Russian Journal of Numerical Analysis and Mathematical Modelling, Volume 30, Issue 6, Pages 313–328, ISSN (Online) 1569-3988, ISSN (Print) 0927-6467, DOI: https://doi.org/10.1515/rnam-2015-0029.

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