TY - JOUR

T1 - Superconvergence of numerical gradient for weak Galerkin finite element methods on nonuniform Cartesian partitions in three dimensions

AU - Li, Dan

AU - Nie, Yufeng

AU - Wang, Chunmei

PY - 2019/8/1

Y1 - 2019/8/1

N2 - A superconvergence error estimate for the gradient approximation of the second order elliptic problem in three dimensions is analyzed by using weak Galerkin finite element scheme on the uniform and non-uniform cubic partitions. Due to the loss of the symmetric property from two dimensions to three dimensions, this superconvergence result in three dimensions is not a trivial extension of the recent superconvergence result in two dimensions Li et al. (0000) from rectangular partitions to cubic partitions. The error estimate for the numerical gradient in the L2-norm arrives at a superconvergence order of O(hr)(1.5≤r≤2) when the lowest order weak Galerkin finite elements consisting of piecewise linear polynomials in the interior of the elements and piecewise constants on the faces of the elements are employed. A series of numerical experiments are illustrated to confirm the established superconvergence theory in three dimensions.

AB - A superconvergence error estimate for the gradient approximation of the second order elliptic problem in three dimensions is analyzed by using weak Galerkin finite element scheme on the uniform and non-uniform cubic partitions. Due to the loss of the symmetric property from two dimensions to three dimensions, this superconvergence result in three dimensions is not a trivial extension of the recent superconvergence result in two dimensions Li et al. (0000) from rectangular partitions to cubic partitions. The error estimate for the numerical gradient in the L2-norm arrives at a superconvergence order of O(hr)(1.5≤r≤2) when the lowest order weak Galerkin finite elements consisting of piecewise linear polynomials in the interior of the elements and piecewise constants on the faces of the elements are employed. A series of numerical experiments are illustrated to confirm the established superconvergence theory in three dimensions.

KW - Non-uniform cubic partitions

KW - Second order elliptic problem

KW - Superconvergence

KW - Three dimensions

KW - Weak Galerkin finite element method

UR - http://www.scopus.com/inward/record.url?scp=85063548373&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2019.03.010

DO - 10.1016/j.camwa.2019.03.010

M3 - Article

AN - SCOPUS:85063548373

VL - 78

SP - 905

EP - 928

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 3

ER -