Abstract
In this paper, we discuss a family of multipoint flux mixed finite element (MFMFE) methods on simplicial, quadrilateral, hexahedral, and triangular-prismatic grids. The MFMFE methods are locally conservative with continuous normal fluxes, since they are developed within a variational framework as mixed finite element methods with special approximating spaces and quadrature rules. The latter allows for local flux elimination giving a cell-centered system for the scalar variable. We study two versions of the method: with a symmetric quadrature rule on smooth grids and a non-symmetric quadrature rule on rough grids. Theoretical and numerical results demonstrate first order convergence for problems with full-tensor coefficients. Second order superconvergence is observed on smooth grids. © 2011 Published by Elsevier Ltd.
| Original language | English (US) |
|---|---|
| Title of host publication | Procedia Computer Science |
| Publisher | Elsevier BV |
| Pages | 918-927 |
| Number of pages | 10 |
| DOIs | |
| State | Published - 2011 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUS-F1-032-04
Acknowledgements: 1 partially 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 under Contract No. DE-SC0001114.2 supported by Award No. KUS-F1-032-04, made by King Abdullah University of Science and Technology (KAUST).3 partially supported by the DOE grant 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.