Antonietti, Paola F., Dedner, Andreas, Madhavan, Pravin, Stangalino, Simone, Stinner, Björn and Verani, Marco (2015) High order discontinuous Galerkin methods on surfaces. SIAM Journal on Numerical Analysis, 53 (2). pp. 1145-1171. doi:10.1137/140957172 ISSN 0036-1429.

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Abstract

We derive and analyze high order discontinuous Galerkin methods for second order elliptic problems on implicitly defined surfaces in R^3 . This is done by carefully adapting the uni-fied discontinuous Galerkin framework of [D. N. Arnold et al., SIAM J. Numer. Anal., 39 (2002), pp. 1749–1779] on a triangulated surface approximating the smooth surface. We prove optimal error estimates in both a (mesh dependent) energy and L^2 norms. Numerical results validating our theoretical estimates are also presented.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Galerkin methods, Differential equations, Partial -- Numerical solutions, Error analysis (Mathematics)
Journal or Publication Title:	SIAM Journal on Numerical Analysis
Publisher:	Society for Industrial and Applied Mathematics
ISSN:	0036-1429
Official Date:	23 April 2015
Dates:	Date Event 23 April 2015 Available 28 January 2015 Accepted 14 February 2014 Submitted
Volume:	53
Number:	2
Page Range:	pp. 1145-1171
DOI:	10.1137/140957172
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	2 June 2016
Date of first compliant Open Access:	3 June 2016
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/H023364/1
Open Access Version:	ArXiv

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