TY - GEN
T1 - A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids
AU - Wheeler, Mary F.
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: 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.
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/597262
UR - https://linkinghub.elsevier.com/retrieve/pii/S1877050911001554
UR - http://www.scopus.com/inward/record.url?scp=79958286564&partnerID=8YFLogxK
U2 - 10.1016/j.procs.2011.04.097
DO - 10.1016/j.procs.2011.04.097
M3 - Conference contribution
SP - 918
EP - 927
BT - Procedia Computer Science
PB - Elsevier BV
ER -