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Volume 13, Issue 5
A New Parallel Finite Element Algorithm Based on Two-Grid Discretization for the Generalized Stokes Problem

Y.-Q. Shang, Y.-N. He & X.-L. Feng

Int. J. Numer. Anal. Mod., 13 (2016), pp. 676-688.

Published online: 2016-09

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  • Abstract

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.

  • Keywords

Generalized Stokes problem, finite element, parallel algorithm, Schwarz method, two-grid method.

  • AMS Subject Headings

65N30, 65N55, 76D07, 76M10

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-13-676, author = {Y.-Q. Shang, Y.-N. He and X.-L. Feng}, title = {A New Parallel Finite Element Algorithm Based on Two-Grid Discretization for the Generalized Stokes Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {5}, pages = {676--688}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/459.html} }
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, finite element, parallel algorithm, Schwarz method, 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.

Y.-Q. Shang, Y.-N. He and X.-L. Feng. (2016). A New Parallel Finite Element Algorithm Based on Two-Grid Discretization for the Generalized Stokes Problem. International Journal of Numerical Analysis and Modeling. 13 (5). 676-688. doi:
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