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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

Online
ISSN
1609-9389
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Volume 11, Issue 4 (Jan 2011)

Issues

Full discretisation of second-order nonlinear evolution equations: strong convergence and applications

Etienne Emmrich
David Šiška

Abstract

Recent results on convergence of fully discrete approximations combining the Galerkin method with the explicit-implicit Euler scheme are extended to strong convergence under additional monotonicity assumptions. It is shown that these abstract results, formulated in the setting of evolution equations, apply, for example, to the partial differential equation for vibrating membrane with nonlinear damping and to another partial differential equation that is similar to one of the equations used to describe martensitic transformations in shape-memory alloys. Numerical experiments are performed for the vibrating membrane equation with nonlinear damping which support the convergence results.

Keywords: evolution equation of second order; time discretization; Galerkin method; convergence; vibrating membrane; shape-memory alloys

About the article

Received: 2011-08-08

Revised: 2011-10-24

Accepted: 2011-11-21

Published in Print:


Citation Information: Computational Methods in Applied Mathematics Comput. Methods Appl. Math., ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.2478/cmam-2011-0025.

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© Institute of Mathematics, NAS of Belarus. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. BY-NC-ND 4.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Riccarda Rossi and Marita Thomas
SIAM Journal on Mathematical Analysis, 2017, Volume 49, Number 2, Page 1419
[2]
Etienne Emmrich and David Šiška
Stochastics and Partial Differential Equations: Analysis and Computations, 2017, Volume 5, Number 1, Page 81
[3]
Etienne Emmrich, David Šiška, and Mechthild Thalhammer
Foundations of Computational Mathematics, 2015, Volume 15, Number 6, Page 1653
[4]
Etienne Emmrich, David Šiška, and Aneta Wróblewska-Kamińska
Mathematical Methods in the Applied Sciences, 2016, Volume 39, Number 10, Page 2449
[5]
Etienne Emmrich and David Šiška
Journal of Differential Equations, 2013, Volume 255, Number 10, Page 3719

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