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Analysis of the discontinuous Galerkin method for elliptic problems on surfaces
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Dedner, Andreas, Madhavan, Pravin and Stinner, Björn. (2013) Analysis of the discontinuous Galerkin method for elliptic problems on surfaces. IMA Journal of Numerical Analysis, Volume 33 (Number 3). pp. 952973. ISSN 02724979

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Official URL: http://dx.doi.org/10.1093/imanum/drs033
Abstract
We extend the discontinuous Galerkin framework to a linear secondorder elliptic problem on a compact smooth connected and oriented surface in ℝ3. An interior penalty (IP) method is introduced on a discrete surface and we derive a priori error estimates by relating the latter to the original surface via the lift introduced in Dziuk (1988). The estimates suggest that the geometric error terms arising from the surface discretization do not affect the overall convergence rate of the IP method when using linear ansatz functions. This is then verified numerically for a number of test problems. An intricate issue is the approximation of the surface conormal required in the IP formulation, choices of which are investigated numerically. Furthermore, we present a generic implementation of test problems on surfaces.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics  
Divisions:  Faculty of Science > Mathematics  
Library of Congress Subject Headings (LCSH):  Galerkin methods, Numerical analysis, Error analysis (Mathematics) , Differential equations  
Journal or Publication Title:  IMA Journal of Numerical Analysis  
Publisher:  Oxford University Press  
ISSN:  02724979  
Official Date:  8 January 2013  
Dates: 


Volume:  Volume 33  
Number:  Number 3  
Page Range:  pp. 952973  
Identifier:  10.1093/imanum/drs033  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
Funder:  Engineering and Physical Sciences Research Council (EPSRC)  
Grant number:  EP/H023364/1  
References:  AINSWORTH, M. & RANKIN, R. (2011) Constant free error bounds for nonuniform order discontinuous Galerkin 

URI:  http://wrap.warwick.ac.uk/id/eprint/57150 
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