TY - JOUR
T1 - A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra
AU - Wheeler, Mary
AU - Xue, Guangri
AU - Yotov, Ivan
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged 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.
PY - 2011/11/6
Y1 - 2011/11/6
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/597324
UR - http://link.springer.com/10.1007/s00211-011-0427-7
UR - http://www.scopus.com/inward/record.url?scp=84859732236&partnerID=8YFLogxK
U2 - 10.1007/s00211-011-0427-7
DO - 10.1007/s00211-011-0427-7
M3 - Article
SN - 0029-599X
VL - 121
SP - 165
EP - 204
JO - Numerische Mathematik
JF - Numerische Mathematik
IS - 1
ER -