Journal
IMA JOURNAL OF NUMERICAL ANALYSIS
Volume 33, Issue 3, Pages 952-973Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imanum/drs033
Keywords
discontinuous Galerkin; interior penalty; surface partial differential equations; error analysis
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Funding
- British Engineering and Physical Sciences Research Council (EPSRC) [EP/H023364/1]
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We extend the discontinuous Galerkin framework to a linear second-order elliptic problem on a compact smooth connected and oriented surface in R-3. 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.
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