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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. 952-973. doi:10.1093/imanum/drs033 ISSN 0272-4979.
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WRAP_Dedner_091013-paperarxiv.pdf - Accepted Version Download (661Kb) | Preview |
Official URL: http://dx.doi.org/10.1093/imanum/drs033
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.
| 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, Numerical analysis, Error analysis (Mathematics) , Differential equations | ||||
| Journal or Publication Title: | IMA Journal of Numerical Analysis | ||||
| Publisher: | Oxford University Press | ||||
| ISSN: | 0272-4979 | ||||
| Official Date: | 8 January 2013 | ||||
| Dates: |
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| Volume: | Volume 33 | ||||
| Number: | Number 3 | ||||
| Page Range: | pp. 952-973 | ||||
| DOI: | 10.1093/imanum/drs033 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Date of first compliant deposit: | 25 December 2015 | ||||
| Date of first compliant Open Access: | 25 December 2015 | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
| Grant number: | EP/H023364/1 |
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