The Library
Adaptive discontinuous Galerkin methods on surfaces
Tools
Tools
Tools
Dedner, Andreas and Madhavan, Pravin (2016) Adaptive discontinuous Galerkin methods on surfaces. Numerische Mathematik, 132 (2). pp. 369-398. doi:10.1007/s00211-015-0719-4 ISSN 0029-599X.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1007/s00211-015-0719-4
Abstract
We present a dual weighted residual-based a posteriori error estimate for a discontinuous Galerkin approximation of a surface partial differential equation. We restrict our analysis to a linear second-order elliptic problem posed on hypersurfaces in R3 which are implicitly represented as level sets of smooth functions. We show that the error in the energy norm may be split into a “residual part” and a higher order “geometric part”. Upper and lower bounds for the resulting a posteriori error estimator are proven and we consider a number of challenging test problems to demonstrate the reliability and efficiency of the estimator. We also present a novel “geometric” driven refinement strategy for PDEs on surfaces which considerably improves the performance of the method on complex surfaces.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Journal or Publication Title: | Numerische Mathematik | ||||||
| Publisher: | Springer | ||||||
| ISSN: | 0029-599X | ||||||
| Official Date: | February 2016 | ||||||
| Dates: |
|
||||||
| Volume: | 132 | ||||||
| Number: | 2 | ||||||
| Page Range: | pp. 369-398 | ||||||
| DOI: | 10.1007/s00211-015-0719-4 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
