Abstract
In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields a positive definite cell-centered system for the pressure by eliminating local velocities. The method is shown to be accurate on highly distorted rough quadrilateral and hexahedral grids, including hexahedra with non-planar faces. Theoretical and numerical results indicate first-order convergence for the pressure and face fluxes. © 2011 Springer-Verlag.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 165-204 |
| Number of pages | 40 |
| Journal | Numerische Mathematik |
| Volume | 121 |
| Issue number | 1 |
| DOIs | |
| State | Published - Nov 6 2011 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUS-F1-032-04
Acknowledgements: Mary Wheeler is supported by the NSF-CDI under contract number DMS 0835745,the DOE grant DE-FG02-04ER25617, and the Center for Frontiers of Subsurface Energy Security underContract No. DE-SC0001114. Guangri Xue is supported by Award No. KUS-F1-032-04, made by KingAbdullah University of Science and Technology (KAUST). Ivan Yotov is partially supported by the DOEgrant DE-FG02-04ER25618, the NSF grant DMS 0813901, and the J. Tinsley Oden Faculty Fellowship,ICES, The University of Texas at Austin.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.