TY - JOUR
T1 - A New Parallel Finite Element Algorithm Based on Two-Grid Discretization for the Generalized Stokes Problem
AU - Y.-Q. Shang, Y.-N. He & X.-L. Feng
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 676
EP - 688
PY - 2016
DA - 2016/09
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/459.html
KW - Generalized Stokes problem
KW - finite element
KW - parallel algorithm
KW - Schwarz method
KW - two-grid method
AB - Based on two-grid discretization, a new parallel finite element algorithm for the
generalized Stokes problem is proposed and analyzed. Motivated by the observation that for
a solution to the generalized Stokes problem, low frequency components can be approximated
well by a relatively coarse grid and high frequency components can be computed on a fine grid,
this algorithm first solves the generalized Stokes problem on a coarse grid, and then corrects
the resulted residual by standard additive Schwarz method on a fine grid. Under some regular
assumptions, error estimates of the approximate solutions are provided. Numerical results are
also given to illustrate the effectiveness of the algorithm.