Error analysis of a space-time finite element method for solving PDEs on evolving surfaces
type: Item
instance of: scholarly article
zbMATH Open document ID: 1307.65120
DOI: 10.1137/130936877
author: Arnold Reusken
author: Maxim A. Olshanskii
published in: SIAM Journal on Numerical Analysis
publication date: 2014-11-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1401.8214
full work available at URL: http://publications.rwth-aachen.de/search
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 58J35
zbMATH DE Number: 6365794
zbMATH Keywords: finite element method
zbMATH Keywords: convergence
zbMATH Keywords: error estimate
zbMATH Keywords: advection-diffusion equation
zbMATH Keywords: moving surface
zbMATH Keywords: numerical example
MaRDI profile type: Publication
OpenAlex ID: W2003977985
arXiv ID: 1401.8214
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title: Error analysis of a space-time finite element method for solving PDEs on evolving surfaces
review text: The authors analyze the finite element method to obtain approximate solutions of the advection-diffusion equation on moving surfaces NEWLINE\[NEWLINE \dot{u}+ (\operatorname{div}_{\Gamma}w)u -v_{d}\Delta_{\Gamma}u =f, \qquad \text{ on } \quad\Gamma (t)\in \Omega \subset \mathbb R^{d},NEWLINE\]NEWLINE NEWLINE\[NEWLINE u(\cdot,0)=0,\qquad \text{ on }\quad \Gamma_{0}= \Gamma (0), NEWLINE\]NEWLINE with the condition NEWLINE\[NEWLINE \int_{\Gamma (t)}u ds = 0\qquad \text{ for }\quad t\in [0,T].NEWLINE\]NEWLINENEWLINENEWLINEUsing the finite element method based on the regular triangulation of \(\Omega \), it is proved that the convergence of the approximate solutions has the first order in an energy norm and second order in a weaker norm. Numerical examples to illustrate this method are not given.
reviewed by: Ivan Secrieru
description: scientific article; zbMATH DE number 6365794