Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 53, Issue 2, Pages 1145-1171Publisher
SIAM PUBLICATIONS
DOI: 10.1137/140957172
Keywords
high order discontinuous Galerkin; surface partial differential equations; error analysis
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Funding
- British Engineering and Physical Sciences Research Council (EPSRC) [EP/H023364/1]
- EPSRC [EP/K038060/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K038060/1] Funding Source: researchfish
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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 unified 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.
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