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Analysis of the discontinuous Galerkin method for elliptic problems on surfaces | OUP Journals & Magazine | IEEE Xplore

Analysis of the discontinuous Galerkin method for elliptic problems on surfaces

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Abstract:

We extend the discontinuous Galerkin framework to a linear second-order elliptic problem on a compact smooth connected and oriented surface in ℝ3. An interior penalty (IP...Show More

Abstract:

We extend the discontinuous Galerkin framework to a linear second-order 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.
Published in: IMA Journal of Numerical Analysis ( Volume: 33, Issue: 3, July 2013)
Page(s): 952 - 973
Date of Publication: July 2013

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